A COMPLETE 

T REATISE 



ON 



PRACTICAL 

LAND-SURVEYING, 

$n J^tbttt Starts: 

Designed chiefly for the 

USE OF SCHOOLS AND PRIVATE STUDENTS. 



By A^NESBIT, 



^ 



Land-Surveyor ; Master of the Classical, Commercial, and Mathematical Academy, 
Oxford-Street, Manchester ; and Author of "A Treatise on Practical Mensuration ;" 
"A Treatise on Practical Guaging;" " Keys to the Mensuration, and Guaging ;" 
"An Introduction to English Parsing, adapted to Murray's Grammar ;" and 
" A Treatise on Practical Arithmetic," &c. &c. 



THE SEVENTH EDITION, 

GREATLY ENLARGED BY NUMEROUS ADDITIONS AND IMPROVEMENTS; 



The whole illustrated by two hundred and fifty Practical 

* 
Examples, one hundred and sixty Wood Cuts, twelve Copper -plates, 

and an Engraven Field-Book of sixteen Pages. 



Sorts 



Printed by Thomas Wilson and Sons, High-Ousegate ; 

FOR LONGMAN, ORME, BROWN, GREEN, AND LONGMANS, 

rATERNOSTER-ROW, LONDON ; AND FOR WILSON AND SONS, YORK. 



1839. 



^ ~£ 



./f + 



5 



Rev. FRANCIS WRANGHAM, M.A.F.R.S. 

Archdeacon of the East Riding of Yorkshire, 
Examining Chaplain to the Archbishop of York, fyc. fyc. 

EMINENTLY DISTINGUISHED FOR HIS HIGH LITERARY 
ATTAINMENTS, 



ZEALOUS SUPPORT OF THE DOCTRINES OF CHRISTIANITY ; 

TO WHOM 

THE AUTHOR OF THIS WORK IS UNDER THE 
GREATEST OBLIGATION, 

THIS EFFORT 

TO RENDER A MOST VALUABLE SCIENCE FAMILIAR 
TO THE MEANEST CAPACITY; 



HUMBLY AND RESPECTFULLY INSCRIBED, 
BY HIS MUCH OBLIGED 

AND MOST OBEDIENT SERVANT, 

A. NESBIT. 

Ml 






re* at Stationers' ffealt 



INTRODUCTION. 



1 he various works which so imperfect a being as man is able 
to perform, and the great advances which he is capable of 
making In the arts and sciences, are astonishing. He comes 
into the world devoid both of strength and of reflection ; nor 
are the powers of his body more rapidly developed, than those 
of his mind. But however ingenious and active the individual 
may prove, when arrived at maturity, his efforts would generally 
be unavailing, if they were not combined with those of his fel- 
lows. His first improvements he acquires from the suggestions 
of his contemporaries, or from the works of his predecessors, 
whose rules and demonstrations have been the labour of ages. 

From the Old Testament, it appears, that the arts and sciences 
were cultivated to a certain extent, before the flood. Among 
the offspring of Cain, Jubal was the father of all such as handled 
the harp and organ ; and Tubal-Cain was the instructor of every 
artificer in brass and iron. According to Josephus, the poste- 
rity of Seth also observed the order of the heavens, and the 
course of the stars. The same author asserts, that the Assyrians 
and Chaldeans were the first, after the deluge, who applied 
themselves to the cultivation of the sciences. Their king, Belus, 
is said to have converted the tower of Babel into an observatory, 
and upon it to have made many astronomical discoveries. 

With regard to the origin of Land-Surveying, historians vary 
in their opinions. Diodorus, Herodotus, and Strabo, attribute 
the invention of it to the Egyptians ; whom they represent as 
constrained by the annual inundation of the Nile, removing or 
defacing their land-marks, to devise some method of ascertaining 
the ancient boundaries after the waters had retired. By Jose- 
phus, however, it is ascribed to the Hebrews. According to 
him, the arts and sciences of Egypt were derived from the pa- 
triarch Abraham, who conveyed them into that country, from 
Ur of the Chaldees. 

The science in question was originally called ' Geometry ;' 
but this being deemed too comprehensive a title for the men- 
suration of superficies, it was afterwards denominated ' The Art 
of Measuring Land.' 

From the banks of the Nile, it was carried into Greece by 
Thales, one of the seven wise men, born before Christ 640 years. 
This philosopher travelled into Egypt, and studied, under its 
sages, astronomy, geometry, and other branches of the mathe- 
matics ; but having given offence to king Amasis, by the free- 

b 



VI INTRODUCTION. 

dom of his remarks upon the conduct of princes, he returned 
home, and employed himself in communicating the knowledge 
which he had acquired. 

The great utility of Land-Surveying, without which it is 
impossible to conduct the affairs of civilized life, induced many 
of the most celebrated philosophers and mathematicians of an- 
tiquity to study its principles ; and to Thales, Pythagoras, So- 
crates, Plato, Aristotle, Euclid, Archimedes, &c. we are indebted 
for many substantial improvements. The ancient Romans, like- 
wise, it is said, held this art in such high veneration, that they 
accounted no man capable of commanding a legion, who was 
incapable of measuring a field. 

The increasing value of land, and the consequent necessity of 
ascertaining its dimensions and content with accuracy, have 
lately called forth many Treatises on this subject ; the principal 
of which we owe to Dix, Davis, Talbot, Crocker, and Cotes ; 
but as these Works take a very limited view of the subject, and 
are, in my opinion, very deficient in practical information, and 
consequently not well adapted either for Schools or private 
Learners, I have been induced to write the following AVork, 
which, I hope, will be found to contain every necessary in- 
struction both on theoretical and practical Surveying. 

I have carefully studied the Works of my predecessors and 
contemporaries ; selected from them such matter as I thought 
most useful ; and combined it with the information that I have 
received from some of the first Land-Surveyors in the kingdom, 
and with my own practical experience for upwards of twenty- 
five years. 

The Work thus compiled and composed, I have divided into 
Seven Parts, upon each of which I shall make a few obser- 
vations. 



Part the First contains such Definitions, Problems, and 
Theorems in Geometry, as I conceived to be indispensably ne- 
cessary in Land-Surveying. Those who desire to see the sub- 
ject more fully treated, are referred to the Elements of Simp- 
son, Emerson, Bonnycastle, Keith, Playfair, and Leslie ; to 
Simson's Euciid, Hutton's Course of Mathematics, and Rey- 
nard's Geometria Legitima. The last AVork is well adapted to 
the capacities of Youth ; and contains a number of Quccstiones 
Solvendw, at the end of each Book ; to which an excellent Key 
has lately been published by the Author. 



Part the Second contains a description of the Chain, Cross- 
Staff, Offset-Staff, Compass, and Field -Book ; also directions 
and cautions to young Surveyors, when in the field ; and a few 
observations relating to Scales, laying down Figures, &c. &c. 

The description of the Compass, together Avith an account of 
the variation of the Needle, has been given, under the convic- 



INTRODUCTION. Vll 

tion that the exact range of some line ought always to be taken, 
in the field, in order to determine the true situation of the 
estate. 

Part the Third treats of the method of surveying with the 
Chain and Cross ; and of measuring Meres, Woods, and Lines 
upon which there are Impediments. 

I am aware that Professional Surveyors seldom or never use 
a Cross ; but I am of opinion that every Learner should be 
taught the use of this instrument, in order to make him ac- 
quainted with the method of forming a right-angle in the 
field ; and to give him a just idea of the nature and properties 
of the base and perpendicular of a triangle. 

In this Part I have exhibited the absurdity of the processes 
frequently adopted by unskilful Surveyors, in computing the 
contents of Narrow Pieces of Land, and of Onsets. Methods 
leading to such erroneous results, ought to be discarded by 
every one who is ambitious of obtaining the appellation of a 
correct Surveyor. 

I have also introduced the method of computing the contents 
of Narrow Pieces of Land, and of Offsets, by means of Equidis- 
tant Ordinates, which will be found more easy, expeditious, 
and accurate, than finding their areas by a succession of tri- 
angles and trapezoids. 

No previous Writer with whom I am acquainted, has given 
this method in such a manner as to make it applicable to general 
practice ; but the Rules which I have laid down may be applied 
with success in all cases when the fences are not very irregular, 
without first measuring the base, in order to divide it into an 
even number of equal parts, which is a general rule given by 
all former Writers on this subject. 

Part the Fourth treats of the method of surveying with 
the Chain only ; and of measuring Meres, Woods, Roads, Rivers, 
Canals, Distances, Lines upon which there are Impediments, 
and Hilly Ground. 

The method of measuring Proof-Lines, in surveying single 
fields, which I have not observed in any preceding publication, 
forms a portion of the subject of this Part. Before I discovered 
this method, I frequently incurred the disagreeable necessity of 
repeating my survey, Avhen disputes took place concernino- the 
measurement. In large surveys, however, I am aware, it has 
long been known and practised by Professional Surveyors. 

In this Part, likewise, I have treated largely upon the sur- 
veying of Hilly Ground, which seems to have been hitherto 
little regarded, and still less understood by the generality of 
Writers on Land-Surveying ; and, to the method of preserving 
the horizontal line by elevating the chain, I have subjoined the 
description and use of King's Quadrant, as well as the mechanism 
and application of one of my own invention. I have also added 

b 2 



Vlll INTRODUCTION. 

a few directions for finding the hypothenusal measure of Hilly 
Ground, for paring, reaping, &c. ; but this generally depends 
upon dividing it into proper figures. 

This subject is closed with a Remark on the impropriety and 
injustice of returning the hypothenusal measure of Hills, uni- 
versally ; although it has been long and strenuously contended 
for, by Theoretical and Superficial Writers. This Remark, 
together with the following Observation, which I have since met 
with, in Professor Leslie's Geometry, second edition, page 
401, will, I think, tend to set this subject completely at 
rest : "In surveying Hilly Grounds, it is not the absolute sur- 
face that is measured, but the diminished quantity which 
would result, had the whole been reduced to a horizontal 
plane. This distinction is founded on the obvious principle, 
that since plants shoot up vertically, the vegetable produce of 
a swelling eminence can never exceed what would have grown 
from its levelled base. All the sloping or hypothenusal distances 
are, therefore, reduced invariably to their horizontal lengths, 
before the calculation is begun." Thus we see the opinion and 
practice of Professional Surveyors approved and supported by 
one of the most profound Mathematicians and Philosophers in 
the United Kingdom. 



Part the Fifth contains four of the most approved methods 
of surveying large Estates or Lordships ; general and particular 
Rules for planning them ; and copious Directions for finding 
their Contents. 

The use of the Parallel Ruler, in straightening crooked 
fences, is also given, in twelve . entirely new Problems, com- 
prising every possible case that can occur in Practice. Several 
methods of copying and reducing Plans have likewise been 
introduced, particularly the description and use of the Penta- 
graph, which instrument far surpasses any other, for that pur- 
pose. 

Three different methods of embellishing Plans are given, con- 
taining directions for shading and colouring Meadows, Pas- 
tures, Corn-fields, Moors, Marshy Grounds, Sands, Rocks, 
Trees, Lakes, Rivers, Sea-Shores, Hills, Pleasure- Grounds, Gar- 
dens, and the Bases and Elevations of Buildings. 

This Part also contains directions for making Compartments ; 
Observations on Penmanship ; and a Plan of a New Town, laid 
out in such a manner as to form straight streets, at right-angles 
with each other, which is by far the most eligible method of 
laying out Building-Ground. An Architectural Elevation of a 
House is likewise given, in order to shew the young Surveyor 
how to proceed, if he should be requested to give a view of the 
buildings belonging to an Estate. 

This Part is illustrated by no fewer than nine copper- 
plates, fourteen wood-cuts, and a neatly engraven Field- 
Book; and it may not be improper to state, that the Estates 



INTRODUCTION. IX 

contained in Plates Eight and Ten, are actual Surveys, taken 
by the Author. 

Part the Sixth contains Rules and Directions for Laying- 
out, Parting-off, and Dividing Land ; illustrated by a greater 
number of examples than I have met with in any other Treatise. 
If any of them should appear superfluous to experienced Sur- 
veyors, they will please to recollect for whom the Work is de- 
signed. 

In parting-off, and dividing land, by means of guess-lines, as 
a difficult branch of the art, I have been particularly explicit ; 
and have exemplified the method by numerous examples, illus- 
trated by figures exhibiting the various lines used in each 
process. 

The method of dividing a Common among various Proprietors, 
according to the different qualities of the Land, has also been 
introduced ; and copious directions have been given for valuing 
land, and conducting an Inclosure. I have likewise inserted 
an Abstract of the General Inclosure Act, which will be found 
to throw more light on the subject of Inclosures, than was «ver 
before given to the Public, in any Treatise on Surveying. 

Indeed, the only Work that takes any notice of Inclosures, 
is one published by Mr. Stephenson, (price sixteen shillings,) 
in which the Author appears to have treated the subject with 
considerable ability. This Work, however, is not at all adapted 
either for Schools or private Learners, as the first principles of 
Land-Surveying are not clearly elucidated. 

As various customary measures prevail in different Counties, 
I have given General and Particular Rules for reducing them to 
statute -measure ; and vice versa. I have also introduced Scotch 
and Irish Land Measure ; by which the Work becomes adapted 
to every part of the United Kingdom. 

Part the Seventh contains the method of measuring and 
planning Villages, Towns, and Cities ; directions for surveying 
and planning Building-Ground, and dividing it into convenient 
lots for Sale ; and Miscellaneous Questions relating to sur- 
veying, laying-out, parting-off, and dividing Land in general. 

Nothing has been said on the method of measuring, planning, 
and laying-out Building-Ground, by any former Writer ; but as 
it is a subject of great public importance, in the vicinity of large 
and improving towns, it ought by no means to be omitted in 
a Treatise on Land-Surveying. 

The Miscellaneous Questions at the end of this Part, win 
serve to exercise the genius of the Learner, after he has acquired 
a competent knowledge of the principles of surveying and di- 
viding Land, by carefully studying the former part of this 
Work. Such Questions tend to rouse the latent energies of 
youth j and to give them a relish for making interesting calcu- 
lations; and a delight in discovering unknown truths. They 

b3 



X INTRODUCTION. 

also call into action those abilities which might otherwise lie 
dormant, for want of objects of sufficient importance to excite 
the curiosity of the ingenious ; and put the powers of their 
minds into motion. 

As the Theodolite is sometimes used in surveying Meres, 
"Woods, Roads, Rivers, and Canals, when angles cannot be taken 
by the Chain, I have given a description of that instrument ; 
but as neither it nor the Plane Table are ever used by Pro- 
fessional Surveyors, when they can avoid it ; and as this Trea- 
tise is confined chiefly to Chain Surveying, I have not given 
any directions for measuring either with the Plane Table or the 
Theodolite. Besides, the expense of these instruments places 
them out of the reach of a great number of those persons who 
may be desirous of learning Surveying ; and as most estates 
may be measured more correctly by the Chain only ; the method 
of surveying of these instruments would only have tended to 
enhance the price of this Work, without adding much to its 
real utility. 

Levelling is a subject in which Writers on Surveying gene- 
rally dabble ; but nothing that I have yet seen, deserves the 
name of a Treatise on Levelling. The only examples worthy 
of notice, are a few in Jones's Treatise on Mathematical Instru- 
ments, selected from the Works of Le Febvre. 

In preparing this Work for the Press, I felt a strong incli- 
nation to comply with the request of my Friends, by saying 
something on the subject of Levelling ; but on mature con- 
sideration, I found that the number of COpper-plates, and the 
quantity of letter-press necessary to do justice to the subject, 
would have too much increased the price of the present Work. 
However, if health and life should permit, I may, perhaps, at 
some future time, turn my attention to this desideratum. 



Having given a brief description of the contents of the fol- 
lowing Work ; it is only necessary to add, that I have endea- 
voured to treat the whole, to the best of my abilities, not only 
in a theoretical, but also in a practical manner. The greater 
part of the Examples for single fields, have been taken from my 
own Field-Books ; consequently, they are such as the Learner 
will generally meet with in taking actual Surveys. Hence, in 
going through this Work, he will become familiar with the 
method of keeping the Field-Book ; so that when he commences 
Field-Practice, he will find no embarrassment in entering his 
Notes. 

Copious directions have been given, in various parts of the 
"Work, for taking the dimensions of all kinds of figures that can 
possibly be met with in the practice of Surveying. This is of 
the greatest importance in measuring ; for it is evident that if 
the dimensions be improperly taken, the results must, of course, 
be incorrect ; notwithstanding the greatest care may be taken 
in laying down the figures, and finding their contents. 



INTRODUCTION. XI 

The engraven Field-Book, being detached from the Sur- 
veying, will also be found extremely convenient in laying down 
the large Surveys ; as it will, probably, be necessary for Learners 
to refer to the lines and stations upon the rough plans. 

In composing the following Work, I have endeavoured to 
consult the wants of the Learner, in every possible way ; con- 
sequently, no information that I conceived to be necessary, has 
been withheld. In order, however, to make a complete Sur- 
veyor, the Rules and Directions which I have laid down must 
be brought into actual use by Field Practice ; not only in mea- 
suring single Fields, but also in surveying large Estates : in 
laying-out, 'parting-off, and dividing Land, and in performing 
every process that occurs in practical operations. 

Being daily employed in the education of Youth, I have had 
many opportunities of observing the numerous difficulties which 
Tutors have to surmount ; it is, therefore, my highest ambition, 
that the following Work may be found well adapted for the use 
of Schools; and be a means of rendering a most useful and 
delightful science familiar to the rising generation. Such as it 
is, I respectfully commit it to the world; trusting that slight 
mistakes will be pardoned, that serious ones have not been in- 
curred, and that the forbearance which I have exercised towards 
the labours of others, will be exercised towards mine in return. 

A. NESBIT. 

Manchester, Aug. 1839. 



P. S. It may, perhaps, be proper to inform the young reader, 
that Professor Leslie, whose opinion I have quoted, in the 
former part of this Preface, concerning the method of measuring 
Hilly Ground, was late Professor of Mathematics, and is now 
Professor of Natural Philosophy, in the University of Edinburgh ; 
and has given to the world several valuable Works, which rank 
him with the first Mathematicians and Philosophers of the Age. 



Mr. NESBIT receives into his House a limited number of 
BOARDERS, for the purpose of Tuition. The Terms of the 
School and other particulars may be known, by applying to 
Mr. NESBIT, Oxford Street, Manchester. 



b 4 



aabrrttsrmrnt 

TO THE SECOND EDITION. 



The flattering Testimonies which the Author has received, 
not only from many of the first Teachers and Mathematicians 
in the kingdom, but also from a considerable number of Pro- 
fessional Surveyors and Commissioners, concerning the merits 
of the First Edition of this AVork, have induced him to revise 
the whole ; and make every Addition and Improvement that he 
thought would render the Second Edition still more acceptable 
to his Friends and the Public. 

Accordingly, it will be found that this Edition is enriched 
with the addition of five new copper-plates ; forty wood-cuts ; 
one hundred and ten new questions : and exceeds the former 
Edition by one hundred and forty pages. And as a much 
smaller type has been chosen, both for the text and the notes, 
the ^v~ork, in its present form, contains nearly twice as much 
matter. 

The Improvements thus introduced, are dispersed through 
the whole of the TVork ; but it may be proper to observe, that 
the method of computing by Equidistant Ordinates ; and of 
measuring and planning Roads, Rivers, and Canals, did not 
appear in the former Edition ; and that Part the Fifth has been 
re-written ; and four of the most approved" methods of surveying 
large Estates, described ; and also illustrated by copper-plates. 

The use of the Parallel Ruler, in straightening crooked fences, 
has likewise been given, in twelve new Problems, comprising 
every case that can possibly occur in Practice. 

The description of the Pentagraph, and its use in copying 
and reducing Plans, have also been added ; together with three 
different methods of making and ornamenting finished Plans. 

Much new and valuable Information has been adduced on the 
method of conducting Inclosures. valuing land, &c. &c. ; and 
an Abstract of the General Inclosure Act inserted, which will 
tend greatly to elucidate the subject. 

Scotch and Irish Customary-Measures have likewise been 
given ; and also the method of measuring by the Gad ; and 
of making an estimation of the number of acres contained in a 
Common, County, or Kingdom. 

Part the Seventh, describing the method of surveying and 
planning Villages, Towns, and Cities; and of measuring, 
planning, and laying-out Building-Ground, is entirely new; 
and will, the Author is persuaded, be found of essential service 
to Learners. 

The Miscellaneous Questions, at the end of this Part, on sur- 
veving, parting-off, and dividing Land, may also be mentioned 
among the Additions and Improvements. 

Bradford, Yorkshire, July. 1820. A. NESBIT. 



C O N T E N T S. 



PART I. 

vJeometrical Definitions • •• ••• •• ... ... l 

Geometrical Problems ••• -•• •■• ... ... 11 

Prob. 1 . To bisect a given line ... ... ... ... 1 1 

2. To bisect a given angle ••• ... ... ... 12 

3. To draw a line parallel to a given line ... ... ... \o 

4. To erect a perpendicular from a given point, near the middle 

of a given line ... ... ... ... ... 13 

5. To erect a perpendicular from a given point, near the end of 

a given line ... ... ... ... ... 13 

6. From a given point, to let fall a perpendicular upon a given 

line ... ••• ... ... ... ,.. 14 

7. To construct a triangle of three given lines ... ... 15 

8. Having given the base and perpendicular, to construct a triangle 16 

9. To describe a square, whose side shall be equal to a given 

right line-. ••• ... ... ... ... jg 

10. To describe a rectangular parallelogram, whose length and 

breadth shall be equal to two given lines ... ... 17 

11. Upon a given right line, to construct a rhombus ... ... 17 

12. With two given right lines, as sides, to construct a rhomboid 18 

1 3. With a given base and two given perpendiculars, to con- 

struct a trapezoid ... ... ... ... ... 13 

14. With four given sides, to construct a quadrilateral figure, 

which has one right angle ... ... ... ... 19 

15. With given transverse and conjugate diameters, to construct 

an ellipse-- ••• ... ... ... ... 19 

16. To reduce a given trapezium, to a triangle of equal area ... 20 

17. To reduce an irregular polygon of five sides, to a triangle of 

equal area •■• ••• • •• ... ... 21 

18. To raise a perpendicular by a scale of equal parts ... 21 

19. To make a right angle by the line of chords on the plane scale 22 

20. To make an acute angle ... ... ... ... 22 

21. To make an obtuse angle ... ... ... ... 23 

22. To find the number of degrees contained in a given angle ... 23 

23. To lay down a line making a given angle with the meridian line 24 

24. Geometrical Theorems ... ... ... ... 26 

PART II 

The Chain ... ... ... ... ... ... ... 32 

The Cross- Staff ... ... ... ... ... ... 33 



Xl> CONTENTS. 

Page. 

The Offset-Staff ... ... ... ... ... ... 34 

The Compass ••• ••• ••■ • •• •• ..35 

The Field-Book -•• ... ••• ••• ... ... 36 

Directions to young Surveyors, when in the Field, &c. ... ... 37 

Directions concerning Scales, laying down Figures, Sac. ... ... 40 

PART III. 

To Survey with the Chain and Cross ... ... ... ... 42 

A Table of lineal measures ■•• •-- • •• ... ... 43 

A Table of square measures... ... ... ... —44 

Prob. 1. Square fields ... ... ... ... ... 45 

2. Rectangular fields ... ... ... ... ... 47 

3. Triangular fields ... ... ... ... .. 48 

4. Fields in the form of a trapezium ... ... ... 51 

5. Fields comprehended under more than four straight sides ... 56 

6. Fields comprehended under any number of crooked sides ... 66 

7. Narrow pieces of land ... ... ... ... 86 

8. Meres and woods ... .. ... ... ... 93 

9. To find the area of a segment of a circle, or any, other curvi- 

lineal figure by means of equidistant ordinates .. . ... 97 

10. To find the breadth of a river ... ... .. ... 107 

1 1 . Lines, upon which there are impediments not obstructing the 

sight ... ... ... ..7 ... ... 108 

1 2. Lines, upon which there are impediments obstructing the 

sight ... ... ... ... ... . . 109 

PAR T IV. 

To Survey with the Chain only ... ... ... ... 110 

MisceUaneous instructions ... .. ... ... ..110 

Prob. 1. Triangular fields ... ... ... ... ... Ill 

2. Fields in the form of a trapezium ... ... ... 122 

3. Fields of more than four sides ... ... ... 142 

4. Meres and Woods ... ... . . ... ... 162 

5. To measure and plan roads, rivers, canals, &c. ... ... 165 

6. To take distances by the chain and scale ... . . 169 

7. To erect a perpendicular by the chain ... ... ... 170 

8. From the plan of a field, and its true area, to discover the 

scale by which it has been constructed ... ... 171 

To measure hilly ground ... ... ... ... ... 172 

Methods used by Practical Surveyors, to reduce hypothenusal to hori- 
zontal lines ... ... ... ... ... 173 

Method I. ... ... ... ... ... ... ... 173 

A Table for reducing hypothenusal to horizontal lines ... . . 174 

A Quadrant for taking the altitudes of hills, steeples, See. .. ... 175 



CONTENTS. XV 

Page. 

To take the altitude of a hill with the Quadrant ■•• ••• -.176 

To take the altitude of a steeple ... ••• ... ••• 176' 

Method II. ... ... ... ■■• ... ••• ... 176 

To preserve the horizontal line by elevating the chain, in ascending or 

descending a hill ... ... ... ••• ••• 176 

Method III. ••• • •• ••• ••• ••• • • 178 

The description and use of King's Quadrant ... •• ••• 178 

A Table, by which a Quadrant (invented by the Author) may be con- 
structed, answering the same purpose as King's •• 181 
The construction of the above Table ... ... ••■ ... 182 

The construction of the Author's Quadrant ••■ ••• ... 182 

The method of proving it • • • • • • • • ■ • • • ... 1 84 

The method of applying it in surveying •• • •-• ••• ... 185 

Methods for finding the hypothenusal measure of hilly ground . . 186 

A remark oil measuring hilly ground ... ... ••• ...191 

PART V. 

To survey farms, large estates, or lordships ... ... ... 195 

First method, by triangles ... ••• ... ••■ •• 195 

Second method, by running lines nearly parallel to each other ... 198 

Third method, by tie-lines, &c ... ... ... ...200 

Fourth method, by running lines in the most advantageous manner, 

without regarding any particular method • • • • - • 200 

Miscellaneous instructions relating to running lines, putting down 
stations, ranging the poles, measuring across valleys, observing 
the fences, &c. &c. ... ... ••• ••• ••• 201 

General rules for planning large surveys ... ••• ... 204 

Directions for planning the estate in Plate VIII. ... ... ... 206 

Directions for planning the estate in Plate X. ... ... ... 207 

Drawing pencils ... ... ... ... ... ... 209 

To compute the contents of estates ... ... ... ... 210 

The use of the parallel ruler, in reducing crooked fences to straight ones, 

in order to find the areas of fields by the method of casting ... 211 
A general rule for the parallel ruler ... ... ... ... 227 

A book of dimensions, castings, and areas, belonging to Plate VIII 228 

Ditto, belonging to Plate X. ... ... ... ... ... 230 

To transfer a rough plan to a clean sheet, in order to make a finished plan 231 
Method I. by points ... ... ... ... ... ... 231 

Method II. by tracing paper ... ... ... ... ... 231 

Method III. by a copying-glass ... ... ... ... 232 

Method IV. by similar squares ... ... ... ... 232 

Method V. by the pentagraph •• • ... ... ... ... 234 

A description of the pentagraph ... ... ... ... 235 



in 



JTTENTS. 



The method of using the pentagraph, In copying and reducing plans . . 

To embellish or fiwMi plain 

Method I. 

To finish plans neatly with Indian ink and colours 

How to choose Indian ink 

Colours necessary for a Land-Surveyor ... 

MjmHH EL 

To finish plans highly with Indian ink and colours 

T. - ale and colour meado" ; 

PasttLT-e-rrr^iii 

C: "-fields ... 

Moors 

Marshy ground 

Sands, rocks, and loose stones 

Trees 

Lakes, rivers, and the sea-shore 

Hilly ground 

Fissure- rrrurls 

The elevations of buildings 

Method III. ... ... ... ..- 

To finish plans highly with Indian ink only 

Shadirg with the pen 

Penmanship... 

Ornaments on Plate IX. 
Ditto on Plate XI. ... 

Miscellaneous ins" "a ting to surveying, planning, eastiz r. 

luing, ice. &c. ... 
A :: rrier of the survey in Plate IX. 



that 

- 

238 

238 

238 

., 
-, 
•241 

241 

... 
.,. 
.-/. 

U 

- 

:-/ 

244 
245 

., 
:-- 

248 
.:. 
250 
25 

::. 

251 



233 



PART VI. 

Directions for laying-out, parting-off, and dividing Land ; and for re- 
ducing Statute-Measure to Customary, and vice versa ; also 
Scofaft and Erieh Measures ... ... ... 251 



SECTION I. 

Pbob. 1. To reduce acres, roods, and perches into square links 8 ; 

'. I : lay out, in a square, any quantity of land proposed 

Opomagma line, to make a rectangle, which shall contain 
any proposed quantity of land ... ... '.' 

4. To lay out any given quantity of land in a rectangle, so that 



CONTENTS. XV11 

Page, 
one of its sides shall be two, three, four, or any number of 
times as long as the other ... ... ... ... 26 1 

Prod. 5. Upon a given base, to lay out a triangle that shall contain any 

given number of acres, &c. ... ... ... ... 262 

6. Upon a given side, or base-line, to lay out a trapezium, which 

shall contain any number of acres ... ... ... 263 

7. Upon a given base, to lay out a rhombus of any content less 

than the square of the base ... ... ... ... 266 

8. To lay out any given quantity of land in a circle ... ... 267 

9. To lay out any given quantity of land in a regular polygon ... 268 

10. To lay out any given quantity of land in an ellipse, with a 

given diameter ... ... ... ... ... 270 

1 1 . To part from a square or rectangle any proposed quantity of 

land, by a line parallel to one of its sides ... ... 272 

12. To part from a square or rectangle any proposed quantity of 

land, either in a right-angled triangle or trapezoid, by a line 
drawn from any of the angles to either of the opposite sides 274 

1 3. To part from a triangle, upon the base or longest side, any 

proposed quantity of land, by a line drawn from either of 
the angles at the base, to the opposite side ... ... 276 

14. To part from a triangle any proposed quantity of land, by a 

line parallel to any of its sides ... ... ... 278 

15. To part from a rectangle or triangle any proposed quantity of 

land, upon a line on which there are offsets, when the area 
of those offsets is to be considered as part of the portion to 
be parted off ... ... ... ... ... 279 

16. To part from a trapezium, or any irregular polygon whatever, 

any proposed quantity of land, by a line drawn parallel to 
any of the sides, or by a line drawn from any of the angles, 
or from any assigned point in one of the sides, to any of the 
opposite sides ... ... ... . . ... 282 

SECTION II. 
Prob. 1 . To divide a square or rectangle, either equally or unequally, 
among any number of persons, by lines parallel to one of 
its sides ... ... ... ... ... ... 291 

2. To divide a triangular field, either equally or unequally, among 
any number of persons, by fences made from any of its 
angles to the opposite side ... ... ... ... 292 

3. To divide a triangular field, either equally or unequally, among 
any number of persons, by fences proceeding from any as- 
signed point in one of its sides ... ... ... 295 

4. To divide a triangular field, either equally or unequally, among 
any number of persons, by fences made parallel to one of 
its sides ... ... ... ... ... ... 297 



XV111 CONTENT.-. 

Page. 
Prob. 5. To divide a trapezium, or an irregular polygon, either equally 
or unequally, among any number of persons, by fences made 
in a given direction ... ... ... ... 300 

6. To divide a common or any quantity of land, of uniform value, 

among: any number of proprietors, in the proportion of their 
respective interests ... ... ... ... 304 

7. To divide a common, <Scc. of variable value, among any number 

of proprietors, in the proportion of their respective interests 306 

Mi~:rllaneous observations on valuing land ... ... ... 307 

Appellations given to commons .. ... ... ... 309 

Directions for setting out new roads, sand-pits, quarries, watering-places, 

kc.&ic. ; and for di%iding commons'and waste lands into allotments 311 
To determine the value of each proprietor's allotment, or claim upon the 

common . . ... ... ... ... ... 313 

To set off,upon the plan,each proprietor's allotment, or share of the common 314 

An example of dividing the common in Plate XII. &c ... ... 314 

A book of quantities, qualities, values, &c. belonging to Plate XII. ... 315 

The operation of finding the value of each proprietor's share of the com- 
mon ; and directions for setting out the allotments in the field 316 
The proof of the division ... ... ... ... ... 317 

Acts of parliament for inclosing commons and waste lands ... ... 313 

An abstract of the general act .. . ... ,.- ... ... 319 

Clauses selected from the special acts ... ... ... ... 333 

SECTION III. 

To reduce statute-measure to customary, and vice versa ... ... 335 

General Rules ... ... ... ... ... ... 336 

Prob. 1. To reduce statute -measure to the customary, of 15 feet to a 

perch, and vice versa ... ... ... ... 337 

2. To reduce statute-measure to the customary, of 18 feet to a 

perch, and v ice vers a ... ... ... ... 340 

3. To reduce statute-measure to the customary, of 21 feet to a 

perch, and vice versa ... ... ... ... 34.3 

4. To reduce statute-measure to the customary, of 24 feet to a 

perch, and v ice versa ... ... ... ... 346 

5. To reduce statute -measure to the customary, of 120 perches 

to an acre, and vice versa ... ... ... ... 349 

General rules for constructing the Tables given in this See;.- n ... 351 

Scotch measure ... ... ... ... ... ... 353 

A Table of Scotch lineal measures ... ... ... ... 353 

A Table of Scotch square measures ... ... .. ... 3.54 

A Table for reducing English to Scotch measure ... ... 354 

A Rule for reducing Scotch to English measure ... . . ... 355 

Irish measure ... ... ... ... ... ... 357 

A Table of Irish lineal measures ... ... ... ... 337 



CONTENTS. XIX 

Page. 
A Table of Irish square measures ... ... ... ... 358 

To reduce Irish to English, or English to Irish measure ... ... 358 

To reduce Scotch to Irish, or Irish to Scotch measure ... ... 358 

The rules for finding the areas of figures, &c. are applicable in all cases 
of laud-surveying, whether the dimensions be taken with an 
'English, Scotch, or Irish chain ... ... ... ... 358 

Examples in English, Scotch, and Irish measures... ... ... 359 

Gad measure ... ... ... ... ... ... 363 

To estimate commons, moors, lordships, counties, or kingdoms, by the 

square mile, &c. ... ... ... ... ... 366 

PAR T VI L 

SECTION I. 

The method of measuring and planning villages, towns, and cities . . . 369 

General directions for taking the dimensions of villages, towns, and cities 370 

Directions for taking the dimensions of the new town in Plate VII. ... 372 

A description of the theodolite .. . ... ... ... ... 374 

Directions for planning villages, towns, and cities.... ... ... 376 

Drawing pencils ... ... ... ... ... ... 377 

Plotting scales ... ... ... ... ... ... 378 

Various plans recommended ... ... ... ... ... 378 

To clean plans or maps ... .. ... ... ... 378 

Indian rubber ... ... ... ... ... ... 379 

Pounce or gum sandarach ... ... ... ... ... 380 

Sponge . . ... ... ... . . ... ... 380 

SECTION II. 
Directions for measuring and planning building-ground, and dividing it 

into convenient lots for sale ... ... ... ... 380 

Directions for taking the dimensions ... ... ... ... 381 

Various examples ... ... ... ... ... ... 382 

Directions for planning, dividing, laying-out, &c. &c. ... ... 386 

House-steads must be of various sizes, according to the respectability 

of the intended buildings ... ... ... ... 387 

Different prices of building-ground ... ... ... ... 387 

SECTION III. 
Miscellaneous questions relating to surveying, laying-out, parting-off, 

and dividing land ... ... ... ... ... 388 

Addenda ... ... ... ... -. 392 

Directions to the Binder for placing the Plates. 

Plate. Page. . Plate. Page. 

I. To face.. •• •• • 34 ! VII. To face .. .. ..248 

II. Ditto .. .. •• • • 180 I VIII. Ditto . . .. -.256 

III. Ditto .. .. •• • • 196 | IX., X., and XI. to follow VIII. agree- 

IV. Ditto . . . • • • . . 198 I ablv to their Numbers. 

V. Ditto .. .- -• .. 236 , XII. To face .. .. ..316 

VI. Ditto .. 242 I 

The Engraven Field-Book to be stitcbed by itself. 



EXPLANATION OF THE PRINCIPAL 

MATHEMATICAL CHARACTERS. 



The sign or character = (called equality) denotes that the re- 
spective quantities, between which it is placed, are equal ; as 4 
poles =: 22 yards z=. 1 chain rr 100 links. 

The sign -+- (called plus, or more) signifies that the numbers, 
between which it is placed, are to be added together ; as 9 + 6 
(read 9 plus 6) = 15. Geometrical lines are generally represented 
by capital letters ; thus A B + C D, signifies that the line C D 
is to be added to the line A B. 

The sign — (called minus, or less) denotes that the quantity 
which it precedes, is to be subtracted; as 15 — 6 (read 15 
minus 6) = 9. In geometrical lines also, A B — C D, signifies 
that the line C D is to be subtracted from the line A B. 

The sign x denotes that the numbers, between which it is 
placed, are to be multiplied together ; as 5 X 3 (read 5 mul- 
tiplied by 3) = 15. 

The sism -f- signifies division; as 15 -f- 3 (read 15 divided 
by 3) = 5. Numbers placed like a vulgar fraction, also denote 
division ; the upper number being the dividend, and the lower 
the divisor ; as ] / =z 5. 

The signs : :: : (called proportionals) denote proportion- 
ality ; as 2 : 5 : : 6 : 15, signifying that the number 2 bears the 
same proportion to 5, as 6 does to 15 : or, in other words, as 2 
is to 5, so is 6 to 15. 

The sign , (called vinculum) is used to connect 

several quantities together; as 9 -j- o'l — 6 > X 2 = 12 — 6"<x 2 = 

6x2 = 12. 

The sign -. placed above a quantity, represents the square of 
that quantity ; as 5-f-3 2 =8 2 — 8x8=64. 

The sign 5 . place d above a quantity, denotes the cube of that 
quantity; as 9 -3~- 8 3 = 12 -8 N3 = 4 3 = 4 y -\ x 4 = 64. 

2 

The sign v ''or ^/, placed before a quantity, denotes the square 
root of that quantity; as v - 9x4 = ^/36 = 6. 

The sign ^/, placed before a quantity, represents the cube root 



of that quantity; as V 6 x 4 x 3^— 8 — ^ 24 x <T - 8 = 
x/72-8 = v/64- 4. 



LAND-SURVEYING. 



ISart tl)e jf tart. 

Definitions? Problems, and Theorems in Geometry, 
requisite in Land-Surveying. 

(jteometry originally signified the art of measuring the 
earth, or any distance or dimensions upon, or within it ; but it 
Is now used for the science of quantity, extension, or mag- 
nitude, abstractedly considered. 



Geometrical Definitions. 

1. A point is considered as having neither length, breadth, 
nor thickness. 

2. A line has length, but is considered as having neither 
breadth, nor thickness ; as A B. 

A B 

3. Lines are either right, curved, or parallel. 

4. A right or straight line, lies wholly in the same direction, 
between its extremities; and is the shortest distance between 
two points ; as A B. 

A B 



2 LAND- SURVEYING. (Part I. 

5. A curved line continually changes its direction, between 
its extremities ; as A B. 




6. Parallel lines always remain at the same distance from each 
other, and though continually produced, would never meet ; as 
A B, C D. 

A ■ B 



1) 




7. A surface or superficies, has length and breadth, but is 

as A B C D. 

G 



considered as having no thickness 



A B 

8. A superficies may be contained within one curved line; 
but cannot be contained within fewer than three straight lines. 

9. The area of a figure, is its superficial content, or the mea- 
surement of its surface. 

10. An angle is the inclination or opening of two lines, having 
different directions, and meeting in a point ; as at A. winch is 
called the angular point ; and, when three letters are used, the 
middle one denotes that point- 




Part I.) LAND-SURVEYING. 3 

11. Angles are of three kinds ; viz. right, acute, and obtuse. 

] 2. A right angle is made by one right line standing perpen- 
dicularly upon another : thus, if D C be perpendicular to A B, 
the angles ADC and C D B are both right angles. 

C 



1) 



B 



13. An acute angle is less than a right angle ; as C A B- 
D 




14. The complement of an angle is what it wants to complete 
a right angle ; as the angle D A B is the complement of the 
angle CAB. 

15. An obtuse angle is greater than a right angle; as B C D. 

B 



D 



16. The supplement of an angle is what it wants of two right 
angles ; as the angle A C B is the supplement of the angle BCD, 

b2 



-i LAND-SURVEYING. (Part I. 

17. A triangle is a figure or superficies, bounded by three 
right lines, and admits of three varieties ; viz. equilateral, 
:.les, and scalene. 



18. An equilateral triangle has all its sides equal ; asABC. 

C 




B 



19. An if triangle has only two of its sides equal; as 

ABC. 

C 




20. A scalene triangle has all it- sides unequal ; as A B C 

C 




LAND-SURVEYING, 



5 



Part I.J 

21. Triangles are also right-angled, acute-angled, and obtuse- 
angled. 

22. A right-angled triangle has one right angle, the side op- 
posite to which is called the hypothenuse, the other two being 
termed legs, or one the perpendicular, and the other the base : 
thus, A C is the hypothenuse, B C the perpendicular, and A B 
the base. 

C 




23. An acute-angled triangle has all its angles acute; as 
ABC. 

C 




24. An obtuse-angled triangle has one obtuse angle; as 
ACB. 

C 




b3 



G 



LAND-SURVEYING, 



(Part 1. 



25. The longest side of any plane triangle is called the base ; 
as A B ; and a line falling upon it, from the opposite angle, at 
right angles, is called a perpendicular ; as C a. 

26. A figure of four sides and angles is denominated a qua- 
drangle or quadrilateral figure. 

27. A parallelogram is a quadrilateral figure, having its oppo- 
site sides parallel and equal ; and admits of four varieties ; viz. 
the square, the rectangle, the rhombus, and the rhomboid. 



28. A square is an equilateral parallelogram, having all its 
angles right angles ; asABCD. 

D € 



B 



29. A rectangle is a parallelogram, having its opposite sides 
equal, and all its angles right angles ; as A B C D. 

D G 



B 



Part I.) LAND-SURVEYING. 7 

30. A rhombus is an equilateral parallelogram, having its 
opposite angles equal ; as A B C D. 




31. A rhomboid is a parallelogram, having its opposite sides 
and angles equal ; as A B C D. 



A 




32. A trapezium is a quadrilateral figure, whose opposite 
sides are not parallel to each other ; as A B C D. 




33. A trapezoid is a quadrilateral figure, having two of its 
opposite sides parallel, and one acute, one obtuse, and two right 



b 4 



8 LAND-SURVEYING. (Part I. 

angles ; as A D, is parallel to B C; the angles at A and B, 
"being right angles. 

c 



B 



34. A diagonal is a right line, joining the two opposite angles 
of a quadrilateral figure, or irregular polygon ; as A B. 




35. Plane figures, having more than four sides, are generally 
called polygons; and receive their particular denominations 
from the numher of their sides or angles. 



36. A pentagon is a polygon of five ; a hexagon of six ; a 
heptagon of seven ; an octagon of eight ; a nonagon of nine ; 
a decagon of ten ; an undecagon of eleven ; and a duodecagon 
of twelve sides > 



37. A regular polygon has all its sides and angles equal, 
"When they are unequal, the polygon is irregular. 



38. A circle is a plane figure, bounded by a curved line, 
called the circumference, which is every where equidistant from 
a certain point within it, called the centre. 



Part I.) LAND-SURVEYING. 9 

39. The circumference of every circle is supposed to be 
divided into 360 equal parts, called degrees ; each degree into 
60 equal parts, called minutes ; and each minute into 60 equal 
parts, called seconds. 




40. The diameter of a circle is a right line drawn through 
the centre, and terminating in the circumference on each side ; 
as A B. 




41. The radius of a circle is half the diameter, or it is a 
right line drawn from the centre to* the circumference ; as A B. 




10 LAND-SURVEYING. (Part I. 

42. An arc of a circle is any part of the circumference ; as 
the arc A B. 




43. A chord is a right line joining the extremities of an arc ; 
as the line A B. 

44. A segment is any part of a circle hounded by an arc and 
its chord. 

45. A semicircle is half of a circle, or a segment cut off by 
the diameter ; as A B C. 




46. A sector is any part of a circle bounded by an arc, and 
two radii. 

47. A quadrant is the fourth part of a circle, or a sector 
bounded by an arc and two radii at right angles to each other ; 
as C D B. 

Corol. Hence a right angle is said to contain 90°. 

Note. — All Definitions and Rules should be committed to memory. 



GEOMETRICAL PROBLEMS. 



PROBLEM I. 



To bisect a given Line A B, 



in 



n 



From A and B as centres, with any radius greater than half 
A B, in your compasses, describe arcs cutting each other in 
m and n. 

Draw the line m C n, and it will bisect A B in 0. 



12 



LAND-SURVEYING. (Part. J. 



PROBLEM II. 



To bisect a given Angle A B C. 
B 




From the point B with any radius, describe the arc A C. 
From A and C with the same, or any other radius, make the 
intersection m. Draw the line B m, and it will bisect the aDgle 
A B C, as required. 



PROBLEM III. 

To draw a Line parallel to a given Line A B, at a given Distance. 

C i- 



o 



-N* 



m 



TO. 



From any two points, m and n, in the given line, with the 
given distance as a radius, describe the arcs r and o. Draw C D 
to touch these arcs, without cutting them, and it will be parallel 
to AB. 

Note. — This problem may be more readily performed by a parallel ruler. 



Part I.) LAND-SURVEYING. 



13 



PROBLEM IV. 

To erect a Perpendicular from a given Point C, near the Middle 
of a given Line A B. 



?v 



m. 



n B 



On each side of the point C, take two equal distances, C m 
and C n ; from m and n as centres, with any radius greater than 
C m or C n, describe two arcs cutting each other in r. Draw 
the line C r, and it will he the perpendicular required. 



PROBLEM V. 

To erect a Perpendicular from a given Point C, near the End 
of a given Line A B. 



,^m 



x* 



iix. 



C B 



From any point m, as a centre, with the radius or distance 
C m, describe an arc cutting the given line in C and n. 

Through n and m, draw a line cutting the arc in r. Draw 
the line C r, and it will be the perpendicular required. 



14 



LAND-SURVEYING. 



(Part I. 



PROBLEM VI. 

From a given Point C, to let fall a Perpendicular upon a given 
Line A B. 



A. 



m 



D 



a. B 



X* 



"With C as a centre, and any radius, a little exceeding the dis- 
tance of the given line, describe an are cutting A B in m and n. 
With the centres m and n, and the same or any radius, exceed- 
ing half their distance, describe arcs intersecting each other 
in r. — Draw the line C r ; and C D will be the perpendicular 
required. 

Note. — The last three problems may be easily performed by a square, or 
a plotting scale. 



Fart I.J LAND-SURVEYING. 15 



PROBLEM VII. 

To make a Triangle with three given Lines, any two of ichich 
must he greater than the third. (Euclid, I. 22. J 

Let the given lines be A B=10, AC=8, and BC=6 chains. 




From any scale of equal parts, (which is to be understood as 
employed likewise in all the following problems,) lay off the 
base A B. 

With the centre A, and radius A C, describe an arc. With 
the centre B, and radius B C, describe another arc, cutting the 
former in C. Draw the lines A C and B C, and the triangle 
will be completed. 

Note. — Any trapezium may be constructed iu the same manner ; having 
the four sides, and one of the diagonals. 



16 



LAND-SURVEYING. 



(Part 7, 



PROBLEM VIII. 

Having given the Base, the Perpendicular, and the Place of 
the Perpendicular upon the Base, to construct a Triangle. 
Let the base A B=9, the perpendicular C D=5, and the 

distance A D=6 chains. 

C 




A D B 

Make A B equal to 9, and A D equal to 6. At D erect the 
perpendicular D C, which make equal to 5. Join A C and B C, 
and the figure will be completed. 

Note. — A trapezium may be constructed in a similar manner, by having 
one of the diagonals, the two perpendiculars let fall thereon from the oppo- 
site angles, and the places of these perpendiculars upon the diagonal. 



PROBLEM IX. 

To describe a Square, whose Side shall be equal to a given right Line. 
Let the given line A B=4 chains. 

:3> C 



A B 

Upon one extremity B of the given line, by Problem V. er 
the perpendicular B C, which make equal to A B. 



erect 



Tart 1.) LAND-SURVEYING. 17 

With A and C as centres, and the radius A B, describe arcs 
cutting each other jn D. Draw the lines A D and C D, and 
the square will be completed. 



PROBLEM X. 

To describe a rectangular Parallelogram^ whose Length and 
Breadth shall be equal to two given Lines. 

Let the length AB = 8, and the breadth B C =: 4 chains. 




At B erect the perpendicular B 0, which make equal to 4. 
With A as a centre, and the radius B C, describe an arc ; and 
with C as a centre, and the radius A B, describe another arc, 
cutting the former in D. Draw the lines A D and C D, and 
the rectangle will be completed. 

PROBLEM XL 

Upon a given right Line to construct a regular Rhombus, 
Let the given line A B = 4 chains. 

3> JC 

K 




A B 

Draw the line A B, equal to 4. With A and B as centres, and 
the radius A B, describe arcs cutting each other in D ; then 

c 



1 8 l axd-nl'rve y : Purt I. 

--.-_ 3 and D as centres, and the same radius, make the 

Draw the lines AD.D C\ and B C. and the rhombus will be 
comple: 

PROBLEM XII. 

-~ ' ' ' -- 9 .crfren, to construct a Rhomboid* 

L - 1 :he given lines beABz:*. and BC = 4 chains. 

D 



/ 



A b B 

Draw the fine A B, equal to 7. Take in yonr compasses the 
fine B C, and lay it from A I : Z — With A and E as centres, and 
the radius A R, make the intersection D. Then with B as a 
centre, and the same radius, describe an arc ; and with D as a 
centre,, and the radius A B. describe another arc, cutting the 
in C. Draw the lines A D. D C. and B G, and the 
will be 



PROBLEM XIII. 

Hazing tie Base and tie turo PerpmeKemiar 

7 

_ the base A B=7. and the perpendiculars B C and A D=u 
and 2 chains respecti 



_ 
B 



Part I.) LAND-SURVEYING. 19 

Draw the base A B, equal to 7, and erect the perpendiculars 
B C equal to 3, and A D equal to 2 chains. Then join D C, 
and the trapezoid will be completed. 

PROBLEM XIV. 

Having the four Sides given, to construct a quadrilateral Figure, 
which has one right Angle. 
Let the sides A B=7, B C=4, C D—6, and D A=3 chains ; 
and let the angle at B be a right angle. 




A B 

Draw the line A B, equal to 7 ; and erect the perpendicular 
B C, equal to 4 chains. With C as a centre, and the radius C D, 
describe an arc ; and with A as a centre, and the radius D A, 
describe another arc, cutting the former in D. Draw the lines 
C D and D A, and the figure will be completed. 

PROBLEM XV. 

Having the transverse and conjugate Diameters given, to construct 
an Ellipsis. 
Let the transverse diameter A B = 7, and the conjugate 
diameter CD = 4 chains. 




20 land-surveying. (Part I. 

Draw the two diameters to bisect each other perpendicularly 
in the centre o. With the radius A o, and the centre C or D, 
intersect A B, in F and f. — These points will be the foci of the 
ellipse. Take any point m, in the transverse diameter, and with 
F and f as centres, and the radius A m, describe the arcs G, G, 
g, g. Then -with the same centres, and the radius B m, describe 
arcs cutting the former in the points G, G, g, g : thus will you 
have four points in the circumference of the ellipse. After this, 
take a second point n, in the transverse diameter, and proceeding 
as before, you will determine other four points. — By the same 
method you may determine as many more as you please ; 
through all of which, with a steady hand, you must draw the 
circumference of the ellipse. 

jsote. — An ellipse may also be constructed as follows: Haying found the 
foci F, f, as before, take a thread equal in length to the transverse diameter 
A B, and fasten its ends, with two pins, in the points F, f ; then stretch the 
thread to its greatest extent ; and by moving a pencil round, within the 
thread, keeping it always tight you will trace out the curve of the ellipse. 

The principle upon which this construction is founded, may be seen in 
Prob, X. Part VL 

PROBLEM XVI. 

To reduce a given Trapezium A B C D, to a Triangle of equal 

Area. 
D 

C 




B E 

Draw the diagonal D B, and parallel to it draw C E, meeting 
A B produced in E. Join the points DE; so shall the triangle 
A D E be equal to the trapezium A B C D. 

Note . — This and the following Problem may be applied in finding the 
areas of trapeziums and irregular polygons by first reducingthemto triangles. 



Part I.) LAND-SURVEYING. 21 

PROBLEM XVII. 

To reduce an irregular Polygon ABCDE, of Jive sides, to a 
Triangle of equal Area. 

C 




Extend the side A E, both ways tit pleasure ; and draw the 
diagonals C E, C A. Parallel to these diagonals draw the lines 
D F, and B G ; join the points C F, G G ; and G C F will be 
the triangle required. 

Note. — Any irregular polygon of more than five sides, may be brought to a 
triangle of equal area, by reducing it successively to a figure with one side less* 
until you bring it to a figure of three sides. Thus the trapezium A B C F, or 
G C D E is equal to the polygon A B C D E, as well as the triangle G C F. 

PROBLEM XVIII. 

To raise a Perpendicular from any point D, in a given Line A B, 
by a Scale of equal Parts. 
C 



f 



5/ 



30L 



m 3 

c 3 



D 



B 



22 LAND-SURVEYING. (Part I. 

Make D m •=. 3 ; and from the points D and m, with the dis- 
tances 4 and .5, describe arcs intersecting each other in n. From 
D, through the points n, draw the line D C, and it will he the 
perpendicular required. 

Note. — This Problem may be performed by any other numbers in the 
same proportion ; but 3, 4, and 5, are the least whole numbers that will 
make a right-angled triangle. 

PROBLEM XIX. 

To make a right Angle by the Line of Chords on the plane Scale. 



JE. 



C 



D 



B 



Draw the unlimited line A B ; then take in your compasses 
60° from the line of chords, and with A as a centre, describe 
the arc E D. Take 90° from the same scale, and set off that 
extent from D to C. Draw the line A C ; and CAD will be 
the angle required. 

PROBLEM XX. 

To make an acute Angle equal to any Number of Degrees ; sup- 
pose 33° 30'. 



E 



S</ 




Part I.) LAND-SURVEYING. 23 

Draw the unlimited line A B ; then take 60° in your com- 
passes, and with A as a centre, describe the arc E D. Then set 
off the angle, 33° 30', from D to C. Draw the line AC; and 
CAD will be the angle required. 

PROBLEM XXI. 

To make an obtuse Angle equal to any number of Degrees; 
suppose 125° 30'. 

c 



J&> 




D B 

Draw the unlimited line A B ; then take 60° in your com- 
passes, and with A as a centre, describe the arc E D, Then 
set off 90° from D to C ; and from C to G set off the excess 
above 90°, which is 35° 30'. Draw the line AG; and G A D 
will be the angle required. 

PROBLEM XXII. 

Tojind the Number of Degrees contained in any given AngWB A. C 

C 



With the chord of 60°, and A as a centre, describe the arc m n. 
Take the distance m n in your compasses, and apply it to the 
line of chords ; and it will show the number of degrees required. 

Note. — Angles may be more expeditiously laid down or measured by 
means of a semi-circle of brass called a Protractor, the arc of which is 
divided into 180 degrees. 

c 4 



24 



LAND-SURVEYING. 



'Part I. 



PROBLEM XXIII. 



To lay dowcn a Line making a aire* Angle ttiik the 
or X&rtk and SoutA Lime. 



1. Lt: if be required to lav down a line that ranges N. E . 
™«lrmg an angle of 45°, with the meridian line. (See the 




Draw the meridian Ene A N ; and with the sweep 1 1 
in your compasses, taken from the line of chords, and A as a 
centre, descrihe the arc B C. 

Set off the given angle 45°, from B : : C : draw the line AC^ 
and it will range X. E. 

Aafe.— If the Hue had ranged >". W, the angle must have bees set off on 
the other siio of the meridian A N : and AD would h*Te been the 



Part I.) LAND-SURVEYING. 25 

2. Lay down a line that ranges S. W. b. W., making an angle 
of 56° 15', with the meridian line. 

Draw the meridian line A S ; and with the sweep of 60° 
describe the arc E F. 

Set off 56° 15' from E to F ; draw the line A F, and it will 
range S. W. b. W., as was required. 

Note 1. — If the line had ranged S. E.b.E., the angle must have been set off 
from E to G ; and A G would have been the direction of the line. 

2. — This Problem will be found useful to young Surveyors, in laying down 
the first line, the range of which should be taken in the field by a compass. 



GEOMETRICAL THEOREMS. 

T'^Dz-. lay besee Elements 

of Euclid. Simpson, and Emerson. 



THEOREM I. 

I B two =:raight lines A B. C D. cut each other in the point E, 
the an^r A E C ^21 be equal to the angle DEB.andC E B 
to A E B. ' Ewr.il I. 15 Simpson La Emerxm L 2 J 




THEOREM II. 

He gmatori side ■:: evarj :riangle is opposite to the greatest 

i^r'-f-, 'iT:-::. I. IS, >':.;: . I. 13. E .. II. 4.^ 

THEOREM III. 

Let the right line E F fall upon the parallel right lines A B, 
C D ; the alternate angles A G- H. G H D are equal to each 
other j and the exterior angle E G B is eqaal to the interior and 
opposite, upon the same ride G H D : and the two interior 
angles B G H, G H D. upon the same side, are together equal 
to nvo right angles, (E :,-;. I. .? v L ?. -£*;/;, I. -i.^ 

E 



A i B 

G 



- D 



\ 



F 



Part I.) 



LAND-SURVEYING, 



27 



THEOREM IV. 

Let A B C be a triangle, and let one of its sides B C be pro- 
duced to D ; the exterior angle A C D is equal to the two in- 
terior and opposite angles CAB,ABC; also the three interior 
angles of every triangle are together equal to two right angles. 
(Euc. I. 32. Simp. I. 9. $ 10. Em. II. 1 $• 2 J 




THEOREM V. 

Let the parallelograms ABCD, DBCEbe upon the same 
base B C, and between the same parallels AE,BC; the paral- 
lelogram ABC D, is equal to the parallelogram D B C E. 
( Euc. I 35. Simp. II. 2. Em. III. 6 J 

A D E 




THEOREM VI. 

Let the triangles A B C, D B C be upon the same base B C, 
and between the same parallels AD,BC; the triangle A B C is 
equal to the triangle D B C. (Euc. 1, 37. Simp. II. 2. Em. II. 10 J 

D 




88 



VKVEYING. 



Par: I 



THE REM VII. 

A B C be a right-angled triangle, Baring die right angle 
lare of the side 6 C is equal to the sum of the 
squares of the sides A B. A _Z" I ' Simp. II 5. 

.Cni.IL 81 








THEOREM VIII. 
Let A I a circle, and B D C an angle of the centre, and 

B A C al 

::r their base; the angle B D C is doable of die angle 

ba>: ::: : 5wny.in.io. £■*.!?. 12 




THEOREM IX 
Let A B C be a semi -circle ; then the 
■■ mi l i ii h, is a rish: angle, 'Ems. III. SI 

: 

B 



A B C in Ant 
Simp III . 




Part I.) 



LAND-SURVEYING. 



29 



THEOREM X. 

Let D E be drawn parallel to B C, one of the sides of the 
triangle ABC; then B D is to D A, as C E to E A. ( Euc. VI. 
2. Simp. IV. 12. Em. II. 12 J 




A D B 

THEOREM XI. 

In the preceding figure, D E being parallel to B C, the 
trianoles A B C, A D E are equi-angular or similar ; therefore 
A B is to B C, as A D to D E ; and A B is to A C, as A D 
to A E. (Euc. VI. 4. Simp. IV. 12. Em. II. 13.J 

THEOREM XII. 

Let A B C be a right-angled triangle, having the right angle 
BAC; and from the point A let A D be drawn perpendicularly 
to the base B C ; the triangles A B D, A D C are similar to the 
whole triangle A B C, and to each other. Also the perpendicular 
ADisa mean proportional between the segments of the base ; 
and each of the sides is a mean proportional between the base 
and its segment adjacent to that side ; therefore B D is to D A, 
asD AtoDC;BCistoBA,asBAtoBD; andBCistoCA, 
as C A to C D. (Euc. VI. 8. Simp. IV. 19. Em. VI. 17 J 




THEOREM XIII. 

Let A B C, A D E be similar triangles, having the angle A 
common to both ; then the triangle A B C is to the triangle 



30 land-surveying. (Part I. 

A D E, as the square of B C to the square of D E. That is 
similar triangles are to one another in the duplicate ratio of 
their homologous sides. ( jEuc.VI.19. Simp.IY. 24<. E?n.ll.l8.J 




THEOREM XIV. 

In any triangle ABC, double the square of a line C D, drawn 

from the vertex to the middle of the base A B, together with 

double the square of half the base A D or B D, is equal to the 

sum of the squares of the other sides A C, B C. (Simp. II. 11. 

Em. II. 28. J 

C 




THEOREM XV. 

In any parallelogram A B C D, the sum of the squares of the 
two diagonals A C, B D, is equal to the sum of the squares of all 
the four sides of the parallelogram. (Simp. II. 12. Em. III. 9. ) 
D C 




THEOREM XVI. 

All similar figures are in proportion to each other as the 
squares of their homologous sides. (Simp. IV. 26. Em. III. 20. ) 

THEOREM XVII. 

The circumferences of circles, and the arcs and chords of 
similar segments, are in proportion to each other, as the radii 
or diameters of the circles. (Em. IV. 8^-9.^ 



Part I.) LAND-SURVEYING. 31 



THEOREM XVIII. 

Circles are to each other as the squares of their radii, diame- 
ters, or circumferences. (Em. IV. 35. ) 

THEOREM XIX. 

Similar polygons described in circles, are to each other, as the 
circles in which they are inscribed ; or as the squares of the 
diameters of those circles. ( Em. IV. 36. ) 

THEOREM XX. 

All similar solids are to each other, as the cubes of their like 
dimensions. (Em. VI. 24.J 



LAND-SURVEYING. 



A Description of the Chain, Cross-Staff, Offset-Staff, 
Compass, and Field-Book ; also Directions and Cau- 
tions to young Surveyors, when in the Field, fyc. 



THE CHAIN. 

JLjand is commonly measured with a Chain, invented by Mr, 
Gunter, which is known by the name of " Gunter's Chain." 

It is 4 poles, 22 yards, or 66 feet in length, and divided into 
100 equal parts, called links ; each link being 7.92 inches. At 
every tenth link from each end, is fixed a piece of brass, with 
notches or points; that at 10 links having one notch or point; 
at 20, two ; at 30, three ; and at 40, four points. At 50, or 
the middle, is a large, round, plain piece of brass. 

The chain being thus marked, the links may be easily counted 
from either end ; the mark at 90, 80, &c. being the same as that 
at 10, 20, &c. Part of the first link, at each end, is made into 
a large ring or bow, for the ease of holding it in the hand. 

The chain should always exceed 22 yards, by an inch and 
half, or two inches ; because, in surveying, it is almost impos- 
sible to go in a direct line, or to keep the chain perfectly 
stretched. Long arrows likewise keep the ends of the chain a 
considerable distance from the ground ; the lines, consequently, 
will be made longer than they are in reality. 



Part II) LAND-SURVEYING. 33 

Chains, when new, are seldom a proper length ; they ought 
always, therefore, to be examined ; as should those, likewise, 
which are stretched by frequent use. 

Note 1. — In folding up the chain, it is most expeditious to begin at the 
middle, and fold it up double. When you wish to unfold it, take both the 
handles in your left-hand, and the other part of the chain in your right ; 
then throw it from you, taking care to keep hold of the handles. You must 
then adjust the links before you proceed to measure. 

2. — Chains, which have three rings between each link, are much better 
than those which have only two ; as they are not so apt to twist. 



THE CROSS-STAFF. 

The Cross-Staff is an instrument used in the field by sur- 
veyors, to erect perpendiculars, and may very easily be made 
in the following manner. 

Procure a piece of board about 6 inches square, either of 
sycamore, box, or mahogany. 

Draw the two diagonals ; and at their extremities fix four 
small studs or pins, which will serve as sights to direct to any 
object or angle. 

Or, instead of studs or pins, you may saw two fine grooves 
at right-angles, about a quarter of an inch deep, in the board. 

This being fixed upon a staff, of a convenient length for use, 
pointed with iron at the bottom to enter the ground readily, 
the instrument is called a cross-staff. 

Note 1. — The cross must be fixed upon the staff by a screw, in such a man- 
ner that it may be easily turned without moving the staff. 

2. — The cross may be made of a circular piece of board ; you must then 
draw two diameters crossing each other at right-angles. The fourth part of 
a square, or of a circle, will answer the purpose equally well. 

3. — Great care ought to be taken in making this instrument, as its accuracy 
depends on the sights, or grooves being at right-angles with each other. 

D 



34 land-surveying. (Part lis 





b 


c 




\ 


/] 


a 


/ 


\ 1 



11 



Suppose a b c d, to represent a cross, and the groove a c to 
be directed to an object at m ; then, "will the groove b d point 
to another at n. 

Reverse the direction of the grooves, so that b d may be in 
the direction of m; then, if a c be in the direction of n, the 
instrument is correct. 



THE OFFSET-STAFF. 

The Offset-Staff is an instrument used to measure short 
distances ; and may be in length. 10, 12, or 15 links. It would 
be advisable to number the links from each end, on opposite 
sides, with the figures, 1, 2, 3, Sec. as the staff, thus marked, 
will be more convenient for use. 

Note. — As the Cross-Staff is sometimes thought incommodious, a small 
pocket-cross may be so contrived as to be readily fixed, upon occasion, to the 
Offset-staff. This may be most expeditiously accomplished by means of a hole 
made through the cross, admitting the top of the staff, to the eighth link, 
counting from the bottom or piked end ; at which place there must be 
attached a small shoulder, upon which the cross will rest. 



Plate I. 



of. tic 



and 
/ 



///r ? //>',//,' '//////'// sv/f//fSf'//// ///////r.j ' 



^rithtlioMrricliaii. 







Part II) LAND-SURVEYING. 35 



THE COMPASS. 

The Compass is an instrument used by surveyors, to point 
out the range or direction of lines ; and also to shew the bear- 
ings of objects. The circumference of the card of the compass 
contains 360°, and is divided into thirty-two equal parts, called 
Points, each containing 11° 15'. 

Of these, the four principal (namely East, West, North, and 
South) are called Cardinal Points ; from which the names of 
the others are derived. 

To the under-side of the card, and in the direction of its north 
and south lines, is attached a magnetic bar of hardened steel, 
called the Needle, by which the north-point is directed toward 
the northern part of the horizon ; and the other points, conse- 
quently, to their corresponding ones in the heavens. 

The card and needle are suspended on an upright pin, called 
the Supporter, which is fixed in the bottom of a brass, or 
wooden, box ; and the whole is covered with a plate of glass to 
prevent the action of the wind upon the card. 

Although the compass is divided into thirty-two points, yet 
surveyors reduce them to eight, namely, the four cardinal, or 
chief points ; and the four midway between them ; viz. the 
north-east, north-west, south-east, and south-west, which may be 
expressed by their initial letters, as E., W. 5 N., S. ; N E., N TV., 
S E., S. W. 

Note 1. — A small pocket-compass may be procured for about five shillings, 
which will answer the purpose of a surveyor ; but for the sake of those who 
may not possess such an instrument, the following methods of finding a meri- 
dian line, &c. are given. When a surveyor enters a field, let him call that 
side, which is next the sun rising, east ; then will the opposite side be west ; 
and, in measuring from the east to the west, he will have the north on his 
right-hand, and the south on his left. If his direction should lie between any 
two of the above points, as for example, between the north and the west, he 
may call the range of the line north-west, &c. This method will suffice, when 
a correct plan is not required. A true meridian, or north and south line, may 
be found by observing which line or fence points accurately toward the sun at 
noon, he being then upon the meridian, or full south. Lines, at right-angles 
to this meridian line, are east and west. 

d 2 



36 land-surveying. (Part II. 

2. — The north point of the compass does not point exactly to the north-point 
of the horizon ; but inclines, in some places toward the east, and in others to- 
ward the west ; and this inclination is called the variation of the compass. In 
most parts of England, the variation is, at this time, more than 24° westerly ; 
so that the true range of any line, or the bearing of any object, will be above 
two points more toward the east than what is indicated by the conr 

This wonderful phenomenon has perplexed our greatest philosophers ; 
neither Halley, nor the immortal Newton, having been able satisfactorily to 
account for it. 

3. — Some compasses have the cards attached to the bottom of the boxes, 
and the needles only are suspended upon pins. When this is the case, place 
the Compass in such a manner that the north -point of the needle may rest 24° 
to the west of the north-point of the card ; and you will thus make an allow- 
ance for the variation ; for in this situation of the Compass, all the points on 
the card, will be in their true positions. 

4. — It is necessary sometimes to get the needle of the Compass retouched 
with the magnet, in order that it may traverse properly ; as the power of 
the magnet, on the needle, has a tendency in lapse of time, to decrease. 



THE FIELD-BOGK. 

Scarcely any two surveyors set down their field-notes exactly 
in the same manner. The method, however, now generally 
adopted, and which is certainly preferable to all others, is to 
begin at the bottom of the page and write upward. 

Each page of the book must be divided into three columns. 
In the middle column must be set down the distances on the 
chain-line at which any mark, oifset, or other observation is 
made : and in the right and left-hand columns respectively, 
those marks, o:Fse:>. an 1 observations must be entered. 

The crossings of fences, rivers, &c. may be denoted by lines 
drawn across the middle column, or part of the right and left- 
hand columns, opposite the distances on the chain-line, at which 
they are crossed ; and the comers of fields, and other remarkable 
turns in the fences, to which oixsets are taken, may be denoted 
by lines joining or lying in the same relation to the middle 
column, as the fences. &c. do to the chain-line. 



Part II.) LAND-SURVEYING. 37 

Thus a tolerably accurate representation of the fences, &c. 
may be sketched in the held, which will very much assist the 
surveyor in drawing the plan. 

With respect to the characters used to denote stations, the 
letters of the alphabet will do very well, in small surveys ; but 
in those of a larger extent, numeral figures must be used, and 
the sign -f- (plus) placed before each figure ; thus, + 1, or -f 2, 
which may be read, station first, or cross first ; station one, or 
cross one, &c. Upon the plan they are generally represented 
by this ( ) mark. 

Most surveyors take the exact range of the first line, and 
enter it in their field-book ; and from it the range of any other 
may be easily determined. This method I shall adopt in the 
following work. 

The expression, R. off B, or L. off B, &c. denotes that you 
are to turn to the right or left-hand, and measure from B, &c. 

Note 1. — Many surveyors not only begin at the bottom of the field-book, 
but also at its right-hand side, and write toward the left, which method I 
always follow myself. 

2. — It is useful for a beginner to draw a rough sketch of the field, or estate 
which he is about to measure ; and upon it, to note the stations in the same 
manner as they are put down in taking the survey. This will materially 
assist his memory in planning. 

3, — The field-book, for practical use, should be made convenient for the 
pocket, and interleaved with blotting-paper. 

4. — The field-notes should always be set down with ink, which may be 
carried in a bottle suspended from a button of your waistcoat. Double foun- 
tain-bottles, such as are used by excise officers, are the best. 

DIRECTIONS and CAUTIONS to YOUNG SUR- 
VEYORS WHEN IN THE FIELD, #C. 

In addition to the instruments already described, you must 
provide ten arroAvs, each about a foot in length, made of strong 
wire, and pointed at the bottom. These should be bent in a 
circular form at the top, for the convenience of holding thenu 
and a piece of red cloth should be attached to each, that they 
may be more conspicuous among long grass, &c. 

d3 



38 LAND-SURVEYING. (Part II. 

Poles, likewise, generally called Ranging-poles, or Station- 
staves, will be wanted as marks, or objects of direction, each 
about ten feet in length, piked with iron at the bottom ; and 
haying a red or white flag at the top, that they may be better 
seen at a distance. Thus equipped, and having entered the 
field, or estate which you are about to survey, first, make your- 
self acquainted with its form ; and then consider in what manner 
you must run your lines, according to the directions hereafter 
given in Parts Third, Fourth, and Fifth : after which you must 
proceed in the following manner. 

Let your assistant or chain-leader take nine arrows in his left- 
hand, and one end of the chain with one arrow in his right ; 
then, advancing toward the place directed, at the end of the 
chain, let him put down the arrow which he holds in his right- 
hand. This the follower must take up with his chain-hand, 
when he comes to it ; the leader, at the same time, putting 
down another at the other end of the chain. In this manner he 
must proceed until he has put down his tenth arrow ; then, 
advancing a chain farther, he must set his foot upon the end of 
the chain, and call out, " change." The surveyor, or chain- 
follower, must then come up to him, if he have no offsets to 
take, and carefully count to him the arrows; and one being 
put down at the end of the chain, proceed as before, until the 
whole line be measured. 

Each change ought to be entered in the field-book, or a 
mistake of 10 chains may happen, when the line is very long. 
The chain-follower ought to be careful that the leader always 
puts down his arrow perpendicularly, and in a right-line with 
the object of direction ; otherwise the line will be made longer 
than it is in reality. The follower may direct the leader by the 
motion of his left -hand ; moving it to the right or left, as cir- 
cumstances require, and always placing his eye and chain-hand 
directly over the arrow which is stuck in the ground. The 
leader likewise, as soon as he has put down his arrow, ought to 
fix his eye upon the object of direction, and go directly toward 
it. This he may easily effect by finding a tree or a bush 
beyond the station to which he is going, and in a straight line 
with it and himself. 



Part II.) LAND-SURVEYING. 39 

In hilly ground, if the follower lose sight of the mark toward 
which he is going, he must stand over his arrow ; and the 
leader must move to the right or left, till he sees the follower 
in a direct line between himself and the mark from which they 
last departed. 

The surveyor ought to put down at each station a small 
stake, called a station-stake, with the number of the station 
upon it ; so that any of the stations may be readily found, if 
there be occasion to measure the distance between two of them, 
as a tie or proof-line, &c. 

In large surveys, there must be a cross cut in the ground, 
at each station, making right-angles with the chain-line ; so 
that, if the stake should be pulled up, the cross may still re- 
main, and serve as a director. 

When a survey is taken with an intent to draw a finished 
plan, all remarkable objects should be noted down in the field- 
book ; as roads, stiles, gates, trees, &c. 

If the surveyor can conveniently procure two assistants, the 
one to lead the chain and the other to follow it, it will be much 
to his advantage ; as he will thus be left at liberty to take 
offsets, note down dimensions, &c. without loss of time. 

He ought always to observe to whom the boundaries belong. 

If the ditch be in the field which he is about to measure, both 
it and the hedge usually belong to the adjoining field. This, 
however, is not always the case ; as it sometimes happens that 
the hedge is on the reverse side of the ditch. It is advisable, 
therefore, to inquire of some person resident on the spot, con- 
cerning the hedges, &c. 

In some places, 3 feet from the roots of the quickwood are 
allowed for the breadth of the ditches ; in some 4, in some 5, 
and in some 6 ; but 4 feet, or 6 links, are commonly allowed 
for ditches between neighbouring estates, and 7 links for ditches 
adjoining roads, commons, waste lands, &c. 

The ditches and fences must always be measured with the 
fields to which they belong, when the whole quantity of land is 
required ; but in measuring crops of corn, turnips, &c. only so 
much must be measured as is, or has been occupied by the 
corn, &c. 

n 4 



40 LAND-SURVEYING. (Part II. 

Upon the surveyor depends all the care of measuring, re- 
marking, noting down, &c. It absolutely behoves him, there- 
fore, to be, not only particularly careful in his entries, and 
correct in his dimensions ; but also extremely accurate in his 
constructions and calculations. 

Note. — The line in which you have the misfortune to lose an arrow, 
must be remeasured. 



DIRECTIONS CONCERNING SCALES, LAYING 
DOWN FIGURES, ftc. 

Any scale of equal parts may be used in planning, or laying 
down figures ; but that, which is most convenient for use, is 
the ivory plotting-scale, so divided on its edges, that you may 
prick off distances by laying it upon the line. 

In la}dng down an offset by the plotting-scale, it is best, first, 
to prick off the base-line ; and then upon it make a small pencil 
dot at every place where a perpendicular must be erected. 

This being done, lay the scale across the base, so that the line 
which goes across the scale, marked with oo, may coincide with 
it, the edge of the scale at the same time touching one of the 
dots. From the dot, by the edge of the scale, draw a line, 
(which will be perpendicular to the base,) and upon it prick off 
the offset ; or it may be pricked off without drawing a line. 

Proceed thus, till all the perpendiculars are erected ; and then 
draw the fence through each of their extremities. If the fence 
be curved, it must be drawn by a steady hand, in the same 
manner as the circumference of an ellipse. (See page \§.) 

In planning, or laying down figures relating to surveying, 
the upper part of the paper or book used should always, if 
possible, represent the north. All the fences and chain-lines 
should first be pencilled : the first should then be drawn, and 
the latter dotted with ink. Great accuracy is required in the 
construction of figures, when the perpendiculars, &c. are to be 
measured by the scale. The lines should be very fine ; the dots 
at the stations very small ; and the points of the compasses very 
sharp, in order that distances may be taken from the scale with 
the utmost correctness. The scale should never be smaller than 



Part III.) LAND-SURVEYING. 41 

two chains to an inch ; for when its divisions are large, figures 
may be constructed with much more accuracy, and their per- 
pendiculars, &c. measured with much greater exactness. 

After having found the area of any field or estate, you may, 
however, lay it down by any scale that will reduce it to a more 
convenient size. Or you may divide the dimensions by 2, 3, 4, 
&c. in order to make them of a proper size to be laid down by 
a scale of 2, 3, or 4 chains to an inch. 

Note 1. — A plotting-scale divided into two chains to an inch on one of its 
edges, and four on the other, is perhaps most useful for a school-boy ; but 
practical surveyors prefer those which have both their edges divided in the 
same manner, because they are more convenient in planning ; and a mistake 
cannot be made by using one edge instead of the other. 

2. — An instrument called a Pricker, which may be made by putting a fine 
needle into a wooden haft, is used by some persons, in pricking off distances 
from the plotting-scale ; but a hard black-lead pencil, finely pointed, is pre- 
ferable, because it does not injure the paper. 



LAND-SURVEYING. 



Part t$t 8$trfc 

To Surrey witk the Chain and Cross; also, to Measure 
Meres, Woods, and Lines upon which there are 
Impediments. 



\^ o>tor jiablt to a statute of 34 Henry VIII. an acre is 
equal to 10 square chains ; that is, 10 chains in length and 1 in 
breadth; or 820 X 22 = 4840 spare yards; or 40 x 4 = 160 
square rods, poles, or perches, 

A statute-pole or perch is 16^ feet long; but in different 
parts of the kingdom there are, by custom, poles of different 
lengths; as 15, IS, 21 feet, 6cc. 

The various dimensions of a piece of land are taken in lineal 
measure, from which its area or content is calculated. 

Nate. — The method of reducing statute -measure to customary, and the 

contrary, may be seen in Part the 5 



Part III.) LAND-SURVEYING, 



43 



A TABLE OF LINEAL MEASURES. 



Inches. 
7.92= 


Link. 
1 








12 


1.5151 = 


Foot. 
1 








Yard. 

1 






36 


4.5454 


3= 


Stat. 






198 


25 


16.5 


5.5= 


Perch. 
1 








Chain. 
1 




792 


100 


66 


22 


4= 






7920 


1000 


660 


220 


40 


10= 


Furl. 
1 




63360 


8000 


5280 


1760 


320 


80 


8 = 


Mile. 
1 



Note. — Seven yards make one rood of fencing or ditching. 



44 



LAND-SUKVEY1NG 



(Part III. 



A TABLE OF SQUARE MEASURES. 





.a 










5 


T— 1 






X 




IT 




« SO 








r- 1 


o 






CD 






CO 












HIS 




*^ S 


(H 


■"f *o 








<N 






CO 




i 




H <j 




II 


O 


© 




tf .§ 




*— < 


© 




-< § 


r— 


lO 




<tf 






CO ^ 




cm' 




CO 




w . 




II 


c 


O IC 




« f£ 




"* 


CD 


© 




^ £ 

& § 


.— 


CD 




r— 


t* 






IH 






CN 






CO ~ 










© 
i— l 








II 


-r 


c 


3 


© 




a- 




00 




-* 


© 




9t 


— . 


«5 


<tf 


SO 


X 


CD 






Oj 




rH 


-r 


b- 






§1 




© 

CO 








© 

CO 








II 


«2 


CD 


— 


c^ 


© 




H 




©q 


IQ 


oa 


CD 


© 




A *5- 


f— 1 


05 




CO 


cc 


i~ 


•^ 




*< s 






<* 


© 


CO 


CO 




13 ti 








:— < 


<* 


00 




CO 














CN 






II 


iH *C 


© 


o 


C 


© 


H . 






cm 


c 


© 


© 


© 


£ ^ 


— 1 


co 


CD 


CO 


c 


o 


c 


© 


^§ 




*0 


cc 




o 


«3 


o 


© 


|3 -IS 




OS 


© 

03 




rt 


CN 


© 


© 


CO 












T— 


© 

CD 




II 


^ 


CO 


-r 


<* 


O 


© 


© 




<tf 


3S 


C 


CO 


CO 


-r 


© 


H ^ 


^T 


1— i 


<N 


(N 


<N 


r— i 


CD 


CD 


tf § 


co 






— 


sc- 


«:• 


Ol 


OS 


<J -<S 


GN 






CO 


CN 


CO 


l> 


00 


t= s 


*> 








CO 


«5 


CM 


^ 


CO ""I 


CD 










—J 


CD 


© 



Part III.) LAND-SURVEYING. 45 

PROBLEM I. 

SQUARE FIELDS. 

TVhen you enter a field which has the appearance of a 
square, (for few are accurately such,) fix your cross-staff in a 
corner of it, and if the two sides be at right-angles, measure 
one of them, and enter its dimensions in your field-book. Pro- 
ceed in like manner with each angle and side ; and if you find 
all the angles right-angles, and all the sides equal, the figure 
is a square. 

TO COMPUTE THE CONTENT. 

Rule. — Multiply the side into itself, and the product will be 
the area, in square links. Cut off five places as decimals, 
toward the right-hand of the product, and those on the left 
will express the number of acres. 

Reduce these decimals into roods and perches, by multiplying 
them successively by 4 and 40, and cutting off five figures 
on the right as before, in each product. 

If the dimensions be in yards, divide the square of the side 
by 4840, and the quotient will be acres. 

Reduce the remainder, if any, into roods and perches, by 
multiplying it successively by 4 and by 40, as before. 

Note 1. — Any person who is not in possession of a chain, may take the 
dimensions in yards, Avhere accuracy is not required. 

2. — In measuring with the chain, it is best to set down the number of links, 
as 956 : where, instead of reading 956 links, read 9 chains and 56 links. 

3. — The dimensions of small parcels of land, sold by the square yard, for 
building, &c. should be taken in feet and inches, with a measuring-tape. 
Paving, digging, &c. should be measured in the same manner. 

4. — In computing the contents of fields, it is customary, among practical 
surveyors, to call the remainder a perch, if it exceeds half a one ; but if it be 
less than half a perch, it is considered as nothing. 

5. — The learner should carefully work over, and put down all the solutions 
given in this book, in order that he may better understand the different 
methods of calculation. 



46 



LAND-SURVEYING. (Part III. 



EXAMPLES. 

1. What is the area in acres of the square ABCD, whose 
side is 956 links ? 

D C 




5736 
4780 
8604 

9.13936 
4 

.55744 
40 



22.29760 Area 9a. Or. 22p. 



2. Required the area in acres of the square, whose side 

264 yards. 264 

264 

1056 
1584 

528 



4840)69696(14 
4840 

21296 
19360 

7T936 

4 

4840)7744(1 
4840 



2904 
40 



484,0)11616,0(24 
968 



1936 

1936 Area 14a. 1r. 24p. 



Part 111.) LAND-SURVEYING. 



47 



3. If the side of a square be 1567 links; what is its area 



in acres f 



Ans. 24a. 2r. 9p. 



4. If the side of a square be 263 yards ; what is its area in 
acres? Ans. 14a. 1r. 6p. 

PROBLEM II. 

RECTANGULAR FIELDS. 

When you enter a field which has the appearance of a rec- 
tangle, try each angle, and measure each side, as before ; and if 
you find all the angles right-angles, and the opposite sides 
equal, the figure is a rectangle. 



TO COMPUTE THE CONTENT. 



Rule. — Multiply the length by the breadth, and the product 
will be the area. 



EXAMPLES. 



1 . What is the area of the rectangle A B C D, whose length 
A B is 1235 links, and breadth A D, 557 links ? 

D C 



B 



1235 
557 
8645 
6175 
6175 

6.87895 
4 

3.51580 
40 

20.63200 Area 6a. 3r. 21p. 



48 land-surveying. (Part III. 

2. Required the area of a rectangle, whose length is 235, 
and breadth 162 yards. 

235 
162 



470 
1410 
235 



484,0)3807,0(7 
3388 



.419 
4 



484)1676(3 
1452 



. 224 
40 
484)8960(18 
484 

4120 
3872 
. 248 Ans. 7a. 3r. J8p. 



3. The length of a rectangular field Is 1225 links, and its 
breadth 613 links ; required the plan and area. 

Area 7a. 2jr. 1p. 

4. If the length of a rectangle be 135, and breadth 50 yards ; 
what is its area ? Ans. 1a. 1r. 23p. 

Note. — As squares and rectangles seldom occur in surveying, it is much 
more expeditious to treat every field of four sides as a trapezium. (See 
Problem 4.) 



PROBLEM III. 

TRIANGULAR FIELDS. 

When you have to survey a field in the form of a triangle, set 
up a pole at each comer, when there are no natural marks. 
Then measure along the base till you come to the point, where 
you think a perpendicular will fall from the opposite angle. 
There plant your cross, and turn its index till the mark at each 



Part III.) LAND-SURVEYING. 49 

end of the base can be seen through one of the grooves. Then 
apply your eye to the other groove, and if you see the mark at 
the opposite angle, you are in the right place to measure the 
perpendicular ; if not, move the instrument backward or for- 
ward, along the line, till you can see the three marks as above 
directed. Enter in your field-book the distance from the end of 
the base to the cross, and the length of the perpendicular. 
Then measure the remainder of the base. 

Note 1 . — Be especially careful, that in measuring the two parts of the 
base and the perpendicular, no confusion of arrows take place. 

2. — In finding perpendiculars by the cross, you must always proceed as 
above directed. 



CONSTRUCTION. 

Having the place of the perpendicular, the figure may be 
easily constructed, as follows. From any scale of equal parts, 
lay off the base ; erect the perpendicular at its proper point ; 
draw a line from each end of the base to the end of the perpen- 
dicular, and the figure will be completed. 

Note. — Having the diagonal, the two perpendiculars, and the place of each 
perpendicular given, you may construct any trapezium in the same manner. 



TO COMPUTE THE CONTENT. 

Rule. — Multiply the base and perpendicular together, divide 
the product by 2, and the quotient will be the area. 

Or, multiply half the base by the whole perpendicular, or 
the whole base by half the perpendicular, and the product will 
be the area, 

examples. 

1. It is required to survey the triangular field ABC, and to 
find its area. 






50 



LAND-SURVEYING. (Part III. 

B 




Measure from A toward C, and when you come to m, for 
instance, at 935 links : try with your cross; and if this be the 
point for the perpendicular, measure m B = 62.5 links. Return 
and measure m C = 628 links, making the whole base = 156'3 
links ; then construct the figure, and find its area. 



1563 base. 
625 per. 




4.88437 

4 

3..53N- 
40 



21.49920 Area 4a. 3r. 21 p. 



2. The distance between the beginning of the base, and 
the place of the perpendicular is 125. the perpendicular 82, 
and the whole base 318 vards ; what is the area of the 



triangle 



Part III.) LAND-SURVEYING. 51 

318 base. 
82 per. 

636 
254*4, 



2) 26076 
4840)13038(2 
9680 



3358 
4 



4840)13432(2 
9680 



3752 
40 



484,0)15008,0(31 
1452 



..488 

484 

77i Ans. 2a. 2r. 31 p. 

3. Measuring along the base of a triangle 862 links, I found 
the true place of the perpendicular, and the perpendicular itself 
= 995 links ; the remainder of the base measured 1110 links; 
what is the area of the triangle ? Ans. 9a. 3r. 10p. 

4. Measuring along the base of a triangular field, I found the 
perpendicular to rise at 865, and its length 645 links ; the re- 
mainder of the base measured 569 links; required the plan 
and area. Area 4a. 2r. 2 Op. 

Note. — If the examples in this Problem, or any of the following Problems, 
be thought too few, more may easily be supplied by the Teacher sketching 
fields, at pleasure, with his pen, which the Learner may measure by a scale. 
This method will be found very advantageous ; as it will give the Learner 
a good idea in what manner he must run his lines, take his dimensions, and 
enter his notes, when he commences field-practice. 



PROBLEM IV. 

FIELDS IN THE FORM OF A TRAPEZIUM. 

A quadrilateral field, having unequal sides, may be surveyed 
by measuring a diagonal. This divides it into two triangles, 
to each of which it serves as a base. 

e 2 



52 



LAND-SUIIVEYIXG. 



(Part III. 



TO COMPUTE THE CONTENT. 

Rule. — Multiply the sum of the two perpendiculars by the 
diagonal, divide the product by 2, and the quotient will be 
the area. 

Note 1. — Always make choice of the longer diagonal, because the longer the 
base line of a triangle, the more obtuse is its subtending angle ; and, conse- 
quently, there is the less chance to mistake, as the perpendicular will be 
shorter, and its place more easily and more accurately determined. After 
finishing the surveying, if you choose, measure the other diagonal, which will 
enable you to prove your work. (See Problems I. and II. Part I V.J 

2. — If a field be very long, or elevated in the middle, so that you cannot see 
from one end to the other, it may be divided into two, or more trapeziums. 
Or you may range your lines over the hill, as directed in Part the Fifth. 

3. — When two perpendiculars cannot be taken upon either of the diago- 
nals, such fields must be divided into two triangles by measuring a diagonal 
for the base of one triangle, and one side of the field for the base of the 
other. (See Example VI.) 

4. — Unskilful surveyors affect to reduce trapeziums into squares, or rect- 
angles, by measuring all the sides, adding each two opposite sides together, 
and taking half their sum respectively for a mean length and breadth ; but 
this method leads to very erroneous results. (See Part IV. Prob. 2.) 

EXAMPLES. 

1. It is required to survey the trapezium A B C D, and find 
its area. 




Part III.) LAND-SURVEYING. 



53 



Measure from A toward C. Finding the perpendicular* a B 
to rise at 473, and its length 437 links ; return, and continue 
toward C, till you come to the place where the second perpen- 
dicular b D rises. There note down its distance from A, 1128 
links ; measure b D = 508 links ; then complete the measuring 
of the diagonal to C, and let the whole be 1490 links. 

After this, measure the diagonal B D, for a proof-line, which 
you will find 1152 links. 

437) 

508JP ei - 

.945 sum. 
1490 diag. 

85050 
3780 
945 

2) 1408050 

7.04025 
4 



0.16100 
40 



6.44000 Area 7a. Or. 6p. 



2. In taking the dimensions of a trapezium, I found the first 
perpendicular to rise at 539, and to measure 725 links ; the 
second at 1890, and to measure 832 links; the whole diagonal 
measured 2456 links; required the area of the trapezium? 

Ans. 19a. Or. 19p. 

3. The first perpendicular of a trapezium rises at 467, and 
measures 545 links; the second at 1418, and measures 467 
links; required its area, the whole diagonal being 1840 links ? 

Ans. 9a. 1r. 9p. 

4. Lay down a field, and find its area, from the following notes. 





A D 






1625 






1252 


523 CL 


B 639 


636 




Begin 


at A. 


Range W. 


. on the left. 


Base 
Line or 


Per. on the right. 




Diag. 


• 


Area 9a. 1r. 


30 £ p. 




E 3 





54 



LAND-SURVEYING 



(Part III. 



5. Required the plan and area of a field, from the following 
dimensions. 





A D 


Diag. 




1744 




545 


1365 






546 


6.52 B. 


egin 


at A. 


Range E. 



Area 10a. 1r. 30p. 



>. Lay down a field, and find its area from the following 



notes. 









D B 




1095 




488 




L. off D. 




AD 


1358 


B .532 410 


Be^in at A. 








Diag. 



298 C. 

Side. 

Ranee E, 



Answer. 

Double areas. 
7224.56 Triangle A B D. 
326310 Triangle BCD. 
Whole area ,5a. Or. 39p. 



ANOTHER METHOD. 



A field of four sides may sometimes be surveyed by dividing 
it into two right-angled triangles, and a trapezoid. 



TO COMPUTE THE CONTENT. 



Rule. — Multiply the sum of the two perpendiculars by their 
distance upon the base-line, and the product will be double the 
area of the trapezoid. The area of each triangle must be found 
as before . 



Part 111.) LAND-SURVEYING. 



55 



EXAMPLES. 

1. It is required to survey the annexed figure, and find its 

area. 

C 




Measure the base A D, and enter in your field-book where 
the two perpendiculars rise, &c. as in the following notes. 

Triangle ABE. 

422 per. 

265 base. 



j 1 


ADr: 1326 


G C = 645 


AG= 952 


IE B = 422 


AE= 265 


i Per. 


Base. 



2110 
2532 
844 

111830 



Triangle GCD. 
645 per. 
374 base. 

2580 
4515 
1935_ 

241230 



Trapezoid E B C G. 
422 \ 
645|P er - 

1067 sum. 
687 base. 

7469 
8536 
6402__ 

733029 



E 4 



56 



LAND-SURVEYING. (Part III. 

733029 



' Double areas 



111- 



collected. 



2)108( 8 

5.43044 

i 

L72i76 

2^" i. lR. 29p. 



2. Required the plan and area of a field, from the foil 



notes. 





AB 






1 z - 1 




E 


1015 


• 1 D. 


G 


132 


705 C. 


Begin 


at A. 


Range W. 


Frr. on the left. 


Base. 


Per. on the right. 



Area 7a. Or. 1'" : p. 

3. Lay down a field, and find its area, from the following 

dimensions. 





AB 














E. 


C SS3 




G. 


Begin 


at A. 


Rang- E 



Area Sa 



PROBLEM V. 



FIELD* COMPREHENDED UXDER MORE THAN 
FOUR STRAIGHT SIDES. 

Avy piece of land, consisting of more than four sides, may 
he surveyed by reducing it into triangles and trapeziums. 

Thus, a field of fire sides mav he reduced into a triangle and 
a trapezium : of six. into two trapeziums ; of seven, into two 

trapeziums and a triangle : of eight, into three trapeziums. &c 



57 



Part III.) LAND-SURVEYING. 

The propriety of dividing fields in this manner, depends 
entirely on the relation which the angles have to one another : 
it is, therefore, sometimes more accurate to divide them into 
triangles. 

TO COMPUTE THE CONTENT. 

Rule. — By the rules given in the last two problems, find the 
double area of each triangle and trapezium contained in the 
figure, 

Collect all the double areas into one sum, which divide by 2, 
and the quotient will be the whole area. 

EXAMPLES. 

1. Lay down a field, and find its area from the following 
notes. 





CE 






1666 


Diag. 




1326 


496 A. 




1000 




D 376 


573 
KoffC 






~KW 


' «* 




1433 


Diag. 




1000 




B 273 


643 




Begin 


at A. 


Range W. 


Per. on the left. 


Diag. 


Per. on the right. 


1> 







\ 




58 land-surveying. (Part III. 



CONSTRUCTION. 

From the notes, the figure obviously consists of five sides, 
and is divided into a triangle and a trapezium. Draw the base 
A C, which make = 1433 links ; at 643 links, let fall the per- 
pendicular a B, upon which lay off 273 links ; join A B and C B, 
and the triangle is completed. Then, with A as a centre, and 
496 links in your compasses as a radius, describe an arc ; and 
with C as a centre, and 1326 as a radius, describe another arc, 
intersecting the former in b. — Through b draw the diagonal 
C E = 1666 links; upon which, at 573 links, erect the per- 
pendicular c D = 376 links. Join C D, D E, and E A, and 
the figure will be completed. 

Note. — If the learner fully comprehend-the above construction, he will not 
find it difficult to lay down the figures belonging to -the following examples ; 
as the same process will succeed in all similar cases. 



Triangle ABC. 

1433 base. 

273 per. 

4299 
10031 

2866 

391209 


Trapezium A C D E 
376 ) 
496 /^ 

872 sum. 
1666 diag. 

5232 
5232 
5232 

872 




391209 ) 
1452752 j 


1452752 




Double areas 
collected. 


2)1843961 






9.21980 
4 






.87920 
40 






35.16800 


Area 9a. Or. 35p. 



Part III.) LAND-SURVEYING. 59 

2. Lay down a field, and find its area, from the following 
dimensions. 



F 400 



D 465 



D 235 



B263 



Begin 



EG 




1150 


Diag. 


1000 




717 




R.offE 




"HE~ 




1474 


Diag. 


1000 




975 




465 


575 G. 


Lk)ffH 




~cW 




1635 


Diag. v * 


1000 




910 


390 1. 


575 




R.offC 




. 


\ 


AC 




1165 


Diag. 


1000 




530 




400 


630 I. 


at A. 


Range E. SE 



60 



LAND-SURVJ£Y1NG. 



Part HI. 




^E 



T:-rZ:-^i A B C I, 

ill ""' 

893 sum. 

1165 diag. 

5358 



• - 



rrarr£-in C D H I 

- 1 ' - 'in 
I 35 diag. 

3 : - : 
1875 

: n :■ 

f-25 



i':4-:-545 



['21-^ 



Part III.) LAND-SURVEYING. 



61 



rapezium 


DEGH. 


Triangle E F G. 


575 


j P er - 




1150 base. 


465 




400 per. 


1040 


sum. 




460000 


, .„, 


drag. 







14/4 




4160 








7280 








4160 








1040 
1532960 










1 040345 ^ 








1021875 ( 


Double areas 




1532960 ( 


collected. 






460000 J 








2)4055180 








20.27590 








4 








1.10360 








40 








4.14400 Area 20a. 1j 


El. 4p. 



3. Required the plan and area of a field, from the following 
dimensions. 



Diag. 





B A 




1008 


E 195 


466 


Return 


to B. 








AD 




1345 


C 415 


944 




855 


Begin 


at A. 








Diag. 

536 B. 
Range W. 



Answer. 

Double areas. 

1279095 Trapezium ABDC. 
196560 Triangle A EB. 
Whole area 7a. 1b. 20ip. 



62 land-surveying. (Part III 

4. Lay down a field, and find its area, from the following 
notes. 





D F 


Diag. 




1940 






1040 


362 B. 


E 581 


825 
R.offD. 






TF 


Diag. 




1488 




C 322 


772 






606 


665 B. 


Begin 


at A, 


Range W 



Answer. 

Donble areas. 

1468656 Trapezium ABDC. 

1829420 Trapezium D E F B. 

Whole area 16a. 1r 38p. 



5. Draw a plan of a field, and find its area, from the following 
dimensions. 



I 382 



E 661 



HK 

m& 

740 

600 

IkoffH. 

~YW 

1223 

803 

666 

L.offF. 



E409 

C 603 
Begin 



D F 

1716 

1080 

761 

R^ftD 

IF 

1547 

1023 

525 

at A. 



Diag. 

162 G. 
Diag. 

276 G. 

Diag. 
246 B. 

Diag. 

488 B. 
Range W, 



Part III.) 



LAND-SURVEYING. 

Answer. 

Double areas. 

1687777 Trapezium A B D C. 

1123980 Trapezium DEFB. 

11459.51 Trapezium F G H E. 

699040 Trapezium HGKI. 

"Whole area 23a. 1r. 5p. 



63 



ANOTHER METHOD. 

A field consisting of five, six, seven, or more sides, may 
sometimes be surveyed by measuring one diagonal, and upon it 
erecting perpendiculars to all the opposite angles, on each side. 
This process will divide the whole field into right-angled 
triangles, and trapezoids, the areas of which must be found as 
before. 

EXAMPLES. 

Lay down a field, and find its area, from the following notes. 



Diag. 





AF 




1896 


E 259 


1342 




1132 




1000 


C367 


763 


B756 


522 


»egin at A. 


Range E. 





325 D. 




64 



LAND-SURVEYING. (Part III. 



Triangle A B a. 
756 per. 
522 base. 



1512 
1512 

3780 
394632 



Trapezoid a B C m. 

»«• 

1123 sum. 
241 base. 



1123 

4492 
2246 

270643 



Trapezoid m C E r. 
367) 
259 j^ 

626 sum. 
579 base. 
5634 
4382 
3130 
362454 



Triangle A D F. 

1896 base. 

325 per. 



9480 
3792 
5688 
616200 



Triangle r E F 


554 base. 


259 per. 


4986 


2770 


1108 


143486 , 



394632 

VJiT-l IDouWe areas 

616200 



2)1 7874 15 

"8.93707 
4 



3.74828 



40 



29.93120 



Area 8a. 3r. 30p. 



2. Lay down a field, and find its area, from the following 
dimensions. 



Part III.) LAND-SURVEYING. 



65 





AK. 





1700 


I 290 


1465 


w 


1368 


r 


1055 


F 144 


986 


m 


794 


e 


515 


C 250 


444 


a 


150 





000 


Begin 


at A. 



Diag. 



d 

365 H 

381 G 

n 

218 E 

350 D 

c 

275 B 



Range W. 



Answer. 

Triangles and Trapezoids on the Right. 
Double areas. 

41250 Triangle A B a. 
228125 Trapezoid a B D e. 
158472 Trapezoid e D E ra. 
156339 Trapezoid m E G r. 
233498 Trapezoid r G H w. 
121180 Triangle w H K. 
938864 sum. 



Triangles and Trapezoids on the Left. 
Double areas. 

111000 Triangle A C c. 
213548 Trapezoid c C F n. 
207886 Trapezoid n F I d. 
_68150 Triangle d I K. 
600584 sum. 

938864 sum brought down. 
1539448 sum total. 



Whole area 7a. 2r. 31 |p. 



3. It is required to lay down a field, and find its area, from 
the following notes. 



66 LAND-SURVEYING. (Part III 



A L. 


Diag. 


2150 





1670 


295 K 


1530 


w 


134.5 


160 H 


1275 


n 


880 


m 


780 


270 E 


465 


150 D 


305 


a 


000 


300 B 


at A, 


Range 



31 460 

d 

I 395 

r 
G 670 
F 400 

e 

c 
C 405 


Begin 



Answer. 

Triangles and Trapezoids on the Right. 

Double areas, 

209250 Trapezoid ABDc. 
132300 Trapezoid c D E e. 
242950 Trapezoid e E H r. 
147875 Trapezoid r H K d. 
141600 Triangle d K L. 



873975 sum. 



Triangles and Trapezoids on the Left, 

Double areas. 

123525 Triangle A a C. 
462875 Trapezoid aCFm, 
422650 Trapezoid m F G n. 
271575 Trapezoid n G I w. 
53(H00 Trapezoid wIML. 

1810725 sum. 
873975 sum brought down. 



2684700 sum total. 



TThole area 13a. 1r. 27f p. 



PROBLEM VI. 

FIELDS COMPREHENDED UNDER ANT NUMBER 

OF CROOKED OR CURVED SIDES. 

When a field is bounded by crooked fences, you must mea- 
sure a line as near to each as the angles or curves will permit : 



Part III.) LAND-SURVEYING. 6'7 

in doing which, you must take an offset to each corner or angle 
in the fence. Where the fences are curved, those offsets must 
be so taken, that a right line drawn from the end of any one 
perpendicular to the end of the next, on each side, would neither 
exclude any part of the land to be measured, nor include any of 
that which is adjacent. Perpendiculars thus erected, will divide 
the Avhole offset into right-angled triangles and trapezoids, the 
areas of which must be found as before. 

Note 1. — If the curves be so large, that many of the offsets would be 2, 3, 
4, or 5 chain long ; it will be more expeditious and accurate, to measure the 
base without taking any offsets, except such as are short, leaving stations in 
proper places along the base, to which, when you have obtained its length, 
you may return, and from them run fresh station-lines, to some convenient 
point, or points, in the curved fence. Upon these lines, take offsets as before. 
(See Example III.) 

2. — If any of the fences be curved inward, it is frequently most convenient 
to measure a line. on the outside of the field, and upon it erect perpendiculars 
to the curved fence, which, in this case, are called insets ; and the area thus 
included must be subtracted from the area of the whole figure. (See Exam- 
ple IV.) 

3. — When the fences and ditches are to be measured with the field to 
which they belong, it is generally most practicable to fix the stations within 
the fences, at a little distance from the corners, and then to measure to the 
roots of the quick-wood ; adding or subtracting 5 or 6 links, according to the 
custom of the place, for the breadth of the ditch. (See Example V.) 

4. — When the offsets are small, their places on the base-line may be deter- 
mined by laying the offset-staff at right angles upon the chain ; but when 
large, and accuracy is required, they must be found by the cross, and mea- 
sured by the chain. 

5. — The base of each triangle and trapezoid, forming an offset, may be 
found by subtracting the distances on the chain-line, from each other. 

6. — The methods frequently used, by unskilful surveyors, to find the area 
of offsets, are very erroneous. Some divide the sum of the offsets by their 
number, for a mean breadth ; others divide that sum by one more than their 
number, for a mean breadth ; and both multiply the whole base by the mean 
breadth, thus supposed to be found, for the area of the whole offset. The 
first of these methods generally gives the area too much ; and the second 
sometimes too much and sometimes too little. A third method, which is 
usually more accurate than either of the preceding ones, is to set down each 

F 2 



68 



LAND-SURVEYING. (Part III. 



offset twice (accounting that one, where the boundary meets the station-line) 
except the first and last, which are only entered once. The sum of these offsets 
is then multiplied by the base, the product divided by the number of offsets 
set down, and the quotient given is the area required. 

7. — Directions for laying down offsets by a plotting-scale, may be seen ia 
Part the Second. 



EXAMPLES. 

1. Lay down the figure of a right-line offset, and find its 
area, from the following notes. 







AB 


n 200 




1569 


m 210 




1249 
1000 


i TO 




952 


e.50 




745 


c 159 




450 


a 120 




265 







000 


egin at 


A 


. Range 



E 




BY THE TRUE METHOD. 



Triangle A r a. 
265 base. 
120 per. 

5300 
265 


Trapezoid r a c s 

279 sum. 
185 base. 


31800 ■ 


1395 
2232 
279 
51615 






Part III.) LAND-SURVEYINGL 

Trapezoid sceu, Trapezoid ueiw. 



69 



per. 



1*9) 
50 j 



209 sum. 
295 base. 



1045 

1881 
418 

6^655 




Trapezoid wimx, 

70) 

210 }per. 


Trapezoid x m n B 
210) 
200/P er - 


280 sum. 
297 base. 


410 sum. 
320 base. 


1960 
2520 
560 

83160 


8200 
123 

131200 



31800 
51615 
61655 1 
24840 
83160 
131200 

2)384270 
1.92135 

4 

3.68540 
40 

27.41600 



Double areas 
collected. 



Hence the true area is 1a. 3r. 27e, 



f3 



70 land-suhveyixg. (Part HI. 

BY THE FIRST FALSE METHOD. 

120 

159 

50 

70 
210 
200 



6)809 



1569 length. 


134.8 breadth. 


12552 


6276 


4707 


1569 



2.11.5012 
134.8 mean breadth. 4 



.460048 
40 

IS. 40 1.9 20 



Here the area appears to be 2a. Or. 18p., which is too much 
by 31 p. 

BY THE SECOND FALSE METHOD. 

120 1569 length. 

159 115.5 breadth. 

™ 7845 

210 1569 

200 1569 ~ 

7)809 1.812195 

115.5 mean breadth. 4 



3.248780 
40 

9.951200 



Here the area appears to be 1a. 3r. 10p., which is too little 
by 17p. 







BY 


THE 


THIRD 


FALSE METHOD. 


o 

120 










1569 length. 
1418 sum. 


120 
159 

159 
50 


12552 
1569 
6276 
1569 


50 

70 

7" 

210 

21" 

200 


12)22.24842 

1.85403 

4 

3.41612 

4" 


1418 


sum 








16.64480 



Part III.) LAND-SURVEYING. 71 

Here the area appears to be 1a. 3r. 16p., which is too little 
by Up. 

2. Lay down a curve-line offset, and find its area, from the 
following notes. 



Begin at 



AB 




1012 





892 


53 


786 


80 


£45 


95 


500 


45 


350 


63 


200 


84 


100 


52 


000 





A. Range 


W. 




52 

100 
5200 No. 1. 



52 
84 

136 
100 



13600 No. 2. 



84 
63 

147 

150 

7350 
147 



63 
45 

108 
150 

5400 
1 08 
16200 No. 4. 



45 
95 

140 
145 

700 
56 
14 



22050 No. 3, 



20300 No. 5, 



95 
80 

175 
141 

175 

700 
175 

24675 No. 6, 



80 
53 

133 
106 

798 



13 



14098 No. 7. 



F 4 



72 



LAND-SURVEYING. (Part III. 



53 
120 

1060 
53 

6360 No. 5. 



Double areas 
collected. 



5200 
13600 
22050 
16200 
20300 
24675 
14098 

6360 

2) 122483 

.61241 
4 
2.44964 
40 



17.98560 Area 2r. 18p. 



3. Lay down the figure of a piece of land adjoining a riyer, 
and find its area, from the following notes. 



Left off F, 



EB 




1350 





1265 


140 a 


1200 


170 


1100 


244 


1000 


250 


900 


190 i 


800 


100 > 


700 


« 


600 





500 


94 


400 


142 


300 


153 


200 


70 


000 





and go 


S W. to 






Part III.) XAND-SURVEYING. 



73 




Return 






H 


50 




110 


g 


154 


cc 


173 




142 







O 

o 





1— 1 




u 


82 m 







P3 


N W. 


to E. 




Triangle B C E. 

1950 base. 
698 per. 

15600 
1755 
1170 



1361100 



74 



LAND-SURVEYING. (Part 111. 



60 

100 
6000 No. 1, 



60 
165 

225 
150 

11250 

225 

33750 No. 2. 



Offsets taken on the line A D. 



110 

70 

180 

100 
18000 No. 3. 



163 
70 



11410 No. 4. 



6000 No. 

33750 

18000 — 
11410 



69160 sum. 



Offsets taken on the line C E. 



82 

200 
16400 No. 1. 


154 
110 

264 
100 


142 

200 


26400 No. 5 


28400 No. 2. 


110 
50 


142 
173 

315 

100 


160 

100 
16000 No. 6, 


31500 No. 3. 


60 
50 


173 
154 

327 
100 

32700 No. 4. 


3000 No. 7. 



16400 No. 

28400 

31500 

32700 

26400 

16000 

3000 



154400 sum. 



Part III.) LAND-SURVEYING. 



75 



Offsets taken on the line E B. 



70 


190 




200 


250 




14000 No. 1. 


440 
100 




70 


44000 No. 


8. 


153 


- 




223 


250 




100 


244 




22300 No 2. 


494 
100 








153 


49400 No. 


9. 


142 

295 






244 




100 


170 




29500 No. 3. 


414 
100 

41400 No. 




142 


10. 


94 







236 


170 




100 


140 




23600 No. 4. 


310 
65 

1550 




94 




100 


186 




9400 No. 5. 


20150 No. 


11 


100 


85 




100 


140 




10000 No. 6. 


3400 
85 




100 


11900 No. 


12 


190 












290 






100 






29000 No. 7. 







14000 No. 

22300 

29500 

23600 

9400 

10000 

29000 

44000 

49400 

41400 

20150 

11900 

304650 sum. 



1. 
2. 
3. 

4. 

5. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 



1361100} Whole 
69160 ( double 
154400 ( areas 
304650 ) collected. 
2) 1889310 

9.44655 
4 



1.78620 
40 

31.44800 



Area 9a. lit. 31 p. 



76 land-surveying. (Part 111. 

4. Lay down a field, and find its area, from the following 



notes. 



Begin at 



C A 




525 


Perpen. 


R.tDffC. 




BC 




846 





600 


64 


400 


85 


200 


50 


000 





R. off B. 




AB 




1253 




1000 




586 


a, the place of the perpen 


A. Range 


W. 




Triangle A B C. 

1253 base. 
525 per. 

6265 
2506 
6265 

657825 



Part 111.) LAND-SURVEYING. 



77 



Insets taken on the line B C. 



50 


85 






10000 


200 


64 






27000 


10000 


149 

200 

29800 






29800 
15744 


50 






82544 


85 






135 


246 








200 


64 








27000 


984 
1476 










15744 










657825 Triangle ABC. 
82544 Insets. 






2)57528 J Difference 










2.87640 










4 










3.50560 






40 










20.22400 Area 2a. 


3r. 


20p. 



Double 

areas 

collected. 



5. Draw a plan of a field, and find its area, from the follow- 
ing notes. 

Diag. 



520 

N. West. 

Fence, 
to A. 





A C 




1155 




1000 


495 


915 




360 


From 


A >g° 


To 


the 


48 


660 


53 


630 


40 


500 


25 


380 


50 


200 


62 


000 


From 


D, g o 



South. 



78 



LAND-SURVEYING. (Part III 



Fence. 




To! 


the 


25 


615 


35 


550 


30 


400 


10 


240 


22 


150 


45 


000 


From 


B,go 


To 


the 


33 


1090 


45 


1045 


56 


800 


40 


500 


48 


300 


30 


000 


»gin at 


A, and 

. . 



to C. 



North. 

Fence. 



toB. 



go West. 




Answer. 
Double areas. 
1172325") Trapezium A B C D. 

98055 I A B ( 

32980 >B C 1 Offsets taken on the 

812541 CD '\ different lines . 



812541 C D') 

58820 IDA! 



"Whole area 7 a. Or. 34|p. 



Part III.) LAND-SURVEYING. 79 

C. La) T down a field, and find its area, from the following 
dimensions. 





EB 






442 







345 


74 




25G 


25 




115 


56 




000 







L. off E. 






CE 






387 







296 


43 




200 


59 




100 


36 




000 






L. off C. 






AC 






1294 


Diag. 




1050 




B 530 


1000 






290 


485 D 




R. off A. 






DA 







567 




32 


458 




67 


364 




24 


235 




43 


123 







000 
R. off D. 






CD 






1116 






1000 




129 


465 




80 + 30 


310 




65 


200 




42 


100 







000 
R. off C. 






BC 






584 


Diag. 


E 293 


328 
R. off B. 





80 



LAND-SURVEYING. 



(Part III 







AB 







1173 


37 




1000 


44 




-900 


78 




750 


46 




600 


85 




400 


42 




200 


o 




000 


in at 


A 


Range 



w. 



I — I 





X 



B 




Answer. 

Double areas. 

1313410 Trapezium A B C D. 
171112 Triangle B E C. 
111401") A B i 
62395 / C D \ Offsets taken 
37326 >DA<; on the 

26805 ICEJ different lines. 
33850JEB t 
Whole area 8a. 3r. 5p. 



7. It is required to lay down a field, and find its area, from 
the following notes. 






III. 




B 


: r. - 








m 
























130 


SHI 




196 


596 






IM 






as 




50 


200 




40 








3 - : 








2 -, 




. >: :• 






m 


. 




:,...-. ■» 




C 








A I 






hoi 




■ 


1 9 ! 1 


















m 






pjpjpj 


































69 












Br 


A. 








: 



82 land-surveying. (Part III 

8. Required the area and plan of a field, from the following 
dimensions. 





AD 






1080 







1000 


40 




950 


60 




890 


5* 




820 


3S 




740 


12 




650 


10 




580 


35 




535 


60 




480 


75 




420 


65^ 




300 


35 




220 


3a 




100 


60 




50 


70 




000 


50 




L. off A, 






C A 






1170 


Diag, 




920 


540 B 


525 


225 






r, off a 






BC 







1065 




25 


1005 




35 


946 




50 


870 




40 


830 




90 


780 




115 


715 




110 


650 




80 


625 




75 


510 




55 


440 




70 


330 




65 


250 




35 


215 




48 


150 




40 


100 




60 


50 




55 


000 
R. off B. 





Part III.) LAND-SURVEYING 



To 


the 





700 


40 


645 


55 


570 


72 


500 


68 


450 


49 


375 


42 


300 


37 


225 


53 


170 


40 


130 


50 


50 


52 


000 


From the 


Fence, 



Fence, 
to B. 



to A. 
go North. 



S3 



Answer. 

Double areas. 

1246050 Trapezium A B C D. 

67710 Offsets taken on the line A B. 
129820 Ditto on the line B C. 
91210 Ditto on the line A D. 
Whole area 7a. 2r. 27f p. 



9. Lay down a field, and find its area, from the following 
notes. 





E A 





500 


18 


450 


40 


400 


74 


350 


08 


300 


04 


250 


80 


200 


35 


100 


20 


50 





000 




R. off E. 



62 



84 



LAND-SURVEYING. 



Parr III 





DE 






20 


550 


50 












110 




94 




110 


.' 




ac 


m 


150 


50 




2S 


50 


°l 


000 


Serum ; 


:: 








;_: 


B 550 


915 




* 




R. off A. 




D A 




; ": 


£ ?:: 






R. offD. 




'"CD 





n 


34 


V 


55 


654 


n 




34 


r : : 




" 


95 


450 




M 


75 


350 




320 


44 


: ' 


40 


i 


30 


50 









1 . : = 



D 



Diag, 



Diag. 



Part III.) 



LAND-SURVEYING. 



85 





BC 





640 


18 


600 


25 


550 


30 


500 


25 


450 


35 


430 


€5 


350 


60 


320 


40 


250 


10 


140 


20 


100 


40 


000 




R. off B. 


To 


the 


€5 


1115 


70 


1075 


60 


1000 


55 


920 


60 


868 


40 


800 


20 


750 


28 


700 


65 


600 


80 


550 


73 


400 


70 


300 


34 


200 


40 


134 


23 


100 





000 


Begin 


at A. 



Fence. 
toB. 



Range W. 



Answer. 

Double areas. 

1310280 Trapezium A B C D. 

281750 Triangle AED. 

116056^ A B 



Offsets taken on the different lines. 



41020 /B C 
83180 >C D 
92400 iDE 
53650J E A 

Whole area 9a. 3r. 22£p. 

g3 



86 land-suhveying. (Part 111. 



PROBLEM VIL 



NARROW PIECES OF LAND. 

The method frequently adopted, is to take breadths in dif- 
ferent places, add all these breadths together, and divide their 
sum by their number, for a mean breadth ; and this supposed 
mean breadth is multiplied by the length, for the area ; but this 
process generally leads to very erroneous results, as the method 
•of finding the mean breadth is void of truth. 

If a piece of land taper regularly from one end to the other, 
you may take its breadth at each end ; half the sum of these 
breadths, will be its mean breadth ; and multiply this mean 
breadth by the length, for the area. But if- it be irregular, you 
must take breadths in the widest and narrowest places, or at 
every particular curve, noting the place of each breadth, upon 
the chain-line. These breadths will divide it into trapezoids, 
which you must compute as before. 

Note 1. — The breadths must he taken directly across the laud to be mea- 
sured, and therefore, if considerable, will require the use of the cross. 

2. — If a piece of land be curved, or longer on one side than on the other, 
by measuring along the middle, you will obtain the true, or mean length. 

3. — When several piecesof land, of various lengths, are contiguous to each 
other, it will generally be most expeditious to measure only one base-line, 
noting the point, where each piece begins and ends, perpendicularly to the 
line. In this case, be especially careful that no confusion take place in 
noting down the breadths of the respective pieces. 

A. — Paring, reaping, &c. both in this and the foregoing problems, should 
be surveyed with a slack chain, in order to obtain the measurement of the 
surface. 

5. — It is best 'to take the first and last breadths of lands or ridges, about 
half a chain from each end, and account them as the end-breadths ; because, 



Part III.) LAND-SURVEYING. 87 

in turning, the plough usually makes some of them appear either broader or 
narrower than they are in reality. It may also be observed that it is fre- 
quently necessary to take the breadths to half a link ; for when the length 
is great, half a link in the breadth is too considerable to be neglected. 

6, — If a narrow piece of land be very irregular, you may obtain its area 
most accurately, by measuring a base-line, in a convenient position ; and, 
upon it, erecting perpendiculars to the boundaries, on each side. 

7. — In surveying with the chain and cross, when the area only of any field 
or piece of ground is required, it is unnecessary to lay down the figure. 



EXAMPLES, 



I. Find the area of a tapering piece of land, whose length 
is 2562 links, and breadth at one end 126, and at the other 
232 links. 



232 f breadths. 
2)358 sum. 

179 mean, 
2562 length. 

~358 

1074 
895 
358 



4.58598 

= 4 

2.34392 
40 



13.75680 Area 4a. 2b. 14p. 



2. Find the area of a piece of land, which is broadest towards 
the middle, from the following dimensions. 



g4 



88 



LAND-SURVEYING. 



(Pari III. 



BY THE TRUE METHOD. 



j 2322 


169 


2000 




1056 


215 


1000 


1 


000 

1 Base. 


125 


Per. 



125 1 
215 / P er - 

340 sum. 
1056 base. 



170 

34 

359040 



215 i 

384 sum. 
1266 base. 

2304 
2304 
768 
384 









359C 

4S6144 | 

2)8451 S4 

4.22592 

4 

.90368 

40 

36^14720 



Double areas 

collected. 



Area 4a. Or. 36p. 



BY THE FALSE METHOD. 



125 i 

215 > breadths. 
169 I 

3)509 

169.6 mean. 



2322 length. 
169.6 breadth. 



13932 
20898 
13932 
2322 

3.93S112 
4 

a 752448 
40 

To. 097 920 



Here the area appears to be 3a. 3r. 30p., which is too little 
by 1r. 6p. 

Again, the dimensions remaining as before, suppose the 
piece to be narrowest towards the middle ; the area by the false 
method will be the same as already found. 






Part III.) LAND-SUIIVEYING. 



89 



BY THE TRUE METHOD. 



2322 
2000 
1056 
1000 
000 
Base. 


"l69~j 

125 i 

215 
Per. 


215 ) 
125/I Jer - 

340 sum. 
1056 base. 

~2040 
170 
- 34 

359040 




125 

169/P er 

294 sum. 

1266 base. 

1? T 64 
1764 
588 






294 
372204 






359040 ) Double areas 
372204 J collected. 






2)731244 










3.65622 










4 








2.62488 








40 










24.99520 







The true area is 3a. 2r. 25p. ; hence the false area is too 
much by 1r. 5p. 

Lastly, the dimensions still continuing, suppose the breadth 
towards the middle to be greater than that at one end, and less 
than at the other ; the false area will still be the same. 



BY THE TRUE METHOD. 



2322 
2000 
1056 



II 10C 



000 
Base. 



125 

169 

215 
Per. 



215 ) 

169/ 



per. 



384 sum. 
1056 base. 

2304 
1920 
384 



405504 



169 
125 



per. 



294 sum. 
1266 base. 

1764 
1764 
588 
294 

372204 



90 



laxd-slrveyixg. (Part III. 



40.5504 
372204 

2)7777^ 

3.SS654 
4 



Double areas 
collected. 



3.5541 1 



40 



22.16640 



The true area is 3a. 3r. 2 2 p. ; hence the false area is too 
much by Sp. 

Thus we see the absurdity of a method which, however, has 
been long practised, and is not yet abolished. 

3. Draw a plan of an irregular piece of land, and find its 
area, from the following dimensions. 





A B 





1325 


246 


1015 




987 




790 


31S 


71S 




560 


223 


465 




345 


346 


266 


372 


000 


From 


A, go 



136 

58 
134 

162 

125 

246 
East. 



A $■.» 







Part III.) LAND-SURVEYING. 



91 



Answer. 

Double areas. 

361176 Offsets on the right. 
684860 Ditto on the left. 

2)1046036 sura. 

T.23018 = 5a. Or. 36|p. the area required. 



4. Find the area of five lands, from the following dimensions. 







2378 


185 


2000 


190 


1700 


194 


1400 


198 


1000 


200 


700 


195 


400 


189 


000 


185 



Area 4a. 2r. 13^ p. 



5. Required the area of six lands, from the following notes. 



3422 


189 


3000 




2500 


204 


2000 




1800 


226 


1000 




800 


191 


000 


165 



Area 6a. 3r. 12p. 



6. Find the area of seven lands, from the following dimensions. 
Note. — In calculating the area, the half -links must be treated as decimals. 



2900 


99£ 


2600 


98J 


2300 


101 


2000 


97A 


1900 


100^ 


1600 


102 


1300 


99h 


1000 


10H 


900 


100 


600 


98i 


300 


100* 


000 


100 




t 



Area 2a. 3r. 23|p. 



92 



LAND-SURVEYING. 



(Part III. 



7. It is required to lay down a narrow piece of land, and 
find its area, from the following dimensions. 





AB 




■:-" 


1230 


460 






250 


60 








918 


300 


25 


800 






690 


235 





500 






440 


108 





•300 






100 


216 


150 




130 


From 


A. go 


N. 




Answer. 




Double area 


5. 




552-:" C 


ffsets on the right. 


14<M 


itto on the left. 




"Whole ar 


-a. 3a. 1r. 35p. 





8. Lay down a field, and find its area, from the following 
notes. 





BC 


: 


521 


70 




97 


300 


99 


200 


78 


100 





000 




R offB. 




AB 





1235 


57 




114 




177 




WW 


500 


232 




252 








rom 


A, go 



521 to C. 

430 

323 

245 

219 

240 

275 

360 

North 






Part III.) LAND-SUltVEYING. 93 

Answer. 
Double areas. 

763685 Offsets on the Right of A B. 
414695 Do. on the Left of A B. 
70270 Do. on the Line B C. 

Area 6a. Or. 38 1 p. 



PROBLEM VIII. 

MERES AND WOODS. 

When you have a mere or wood to survey, by the help of 
your cross, fix four marks on its out side, in such a manner as 
to form a rectangle or square. Then measure each side of the 
rectangle or square, taking insets to the edge of the mere or 
wood, the area of which must be treated as directed in Note 2, 
Prob. VI. 

If the opposite sides be not found equal, or very nearly so, 
your marks do not form four right angles ; in which case, you 
must rectify your error. 

Note 1 . — It is a more expeditious method to measure the four sides of a 
quadrilateral figure, having one right angle, paying no regard to the length 
of the sides. Then construct the figure by Part I. Prob. XIV. ; and draw 
the longer diagonal, upon which let fall a perpendicular from each of the 
pposite angles. This diagonal, and these perpendiculars you must measure 
by the scale used in plotting. 

2. — It sometimes happens, that the mere or wood is of a triangular form ; 
in this case, the work may be very readily done, by measuring the three 
sides of a triangle, taking insets as before. After which construct the tri- 
angle, and from the opposite angle let fall a perpendicular upon the base, 
and proceed as before. 

3. — By this problem you may measure fields into which you are not per- 
mitted to enter, or which contain obstructions. 



94 



RVEYING, Pm f III. 






1. Let the following figure re . mere; : 

required. 

C D 




Having fixed four mark?. A. B. C. and D. forming a reefc- 

angle ; begir_ at A. and measure the line A B, taking the ne- 
cessary insets, and entering them in your field-book. In Qie 
same manner proceed with the : tha three a irs ; and you inll 
find noted the following di-rr -- nans. 



AD 




11 


: 


: ■ :■•-» 




>■::> 


50 


' " 


re 


, : : :■ 


61 




I 


R. oBD 










Part III.) LAND-SURVEYING. 



95 



Begin at 



CD 




1450 





1200 


70 


1000 


80 


820 





GOO 





400 


95 


110 


150 


000 





R. off C. 




BC 




1100 





950 


110 


700' 


70 


550 


142 


300 


100 


000 





R. off B. 




AB 




1450 





1200 


55 


1000 




900 


15 


550 


32 


250 


65 


000 





A. Range 


W. 



Answer. 



1595000 Area of the rectangle A B C D. 

135550^ AB r 

183800 (B C J Double areas of the insets taken on the 
168450 ( C D) different lines. 

95500 ) D A( 
2) 5833 00 

291650 Area of the whole insets. 



13.03350 Ditto of the mere. 

4 



.13400 
40 

5.36000 



Area 13a. Or. 5p. 



9*> 



LAND-SURVEYING. (Part III. 



2. Let the following figure represent a wood ; its area is 
required. 

B 




Set up your cross at A, and let your assistant fix the marks B 
and D, so that the angle at A may be a right angle ; and mea- 
sure the line A B, taking insets as before. Then fix the mark 
C, as most convenient ; measure the, other three lines, and you 
will find in your field-book the following notes. 





DA 





1550 


160 


1440 


50 


1200 




1000 





900 




L. off D. 




CD 





950 


120 


'500 





000 




L. off C. 



Part III.) LAND-SURVEYING. 



97 





BC 




1340 





1050 




1000 


50 


700 


60 


400 





000 




L. off B. 




Tb" 





1150 




1000 


50 


900 





550 


100 


300 


110 


160 





000 


Begin at 


A. Range 

1 



N. 



Answer. 
Having constructed the figure, you will find the diagonal B D 
to measure 1930, the perpendicular A a 923, and C a 605 links, 

Double areas. 
2949040 Trapezium A B C D. 
"102000^ AB/ 
114000 / C T)\ * nsets ta ^ en on tne different lines, 

83000 ) Di( 
373 500 Whole Insets, 

Area 12a. 3r. 20p. 



2575540 Wood. 



PROBLEM IX. 

To find the Area of a Segment of a Circle, or any other Cur- 
vilineal Figure, by means of Equidistant Ordinates, 

RULE. 

If a right line A N be divided into any 
even number of equal parts A C, C E, E G, 
&c. ; and at the points of division be 
erected perpendicular ordinates A B, C D, R 
E F, &c. terminated by any curve B D F, / 
&c. ; and if A be put for the sum of the ex- J 
treme or first and last ordinates, A B, N O ; 

H 



KMO 



A C EG I L N 



OS i... YiNvr. Pet 111. 

B for the sum of the even ordinate? C D, G. H. L M. \ 
the second, four sum of all the rest 

E F. I K. &c fix. : rliird, filth, &e.. or the odd ordinates, 
wanting the first and las: the common distan: A. '. h 

C E. & : of the ordinates, being multiplied by the sum arising 
from the addition of A, four times B. and two times C ; one- 
third of the product will be the area A B O X. very nearly ; that 

A — -» B — ° C 
is. - — — xDr the area, putting D = A t 

•3 

common distance of the ordinates. 

Note. — The foregoing rule being expressed in an algebraic form, is seldom 
properly understood by learners ; but the following one may be easily com- 
prehended and committed to memory. 



KULK. 

T :he sum of the first and last ordinates, add four tin: 
sum of all -rdinates, and twice the sum of all the odd 

ordinates, not including the first and last^ multiply th: 

r commoi of the ordinates, divide the product 

by 3, and the quotient will be the area required. 

Note. — The length of the base must be ascertained before yon begin to 
take the ordinates, in order that yon may divide it into an even number of 
equal parts ; or you may take the dimensions without doing this, and find 

:'.1t ire;-.= ::' : r jir: — :: :he e:.i. ":; ...i rulr: ::r :r:i: j.t- „:.£ rr-^Tri:::~. 
which being added to that part of the figure computed by equidistant ordi- 
nates, will give the whole area. See the following example. 



1 . Required the plan and area of a piece of land, measured 
by equidistant ordinate?, from the following notes. 



Part III.) LAND-SURVEYING, 



99 



Besfin 



AB 




1167 





1100 


44 EF 


1000 


97 CD 


900 


139 


800 


175 


700 


206 


600 


230 


500 


248 


400 


260 


300 


264 


200 


268 


100 


262 


000 


252 


at A, and 


go West 




E C 



The first and last ordinates. 

252 The first ordinate A G. 
97 The last ordinate C D. 
349 Sum. 



The even ordinates. 

262 Second. 
264 Fourth. 
248 Sixth. 
206 Eighth. 
139 Tenth. 

TTl9 Sum. 
4 

4476 Four times the sum. 



h 2 



100 land-surveying. (Part III. 



The odd ordinates, 

268 Third. 
260 Fifth. 
230 Seventh. 

175 Ninth. 
933 Sum. 



1866 Twice the sum. 



349 The first and last ordinatef> 
4476 Four times the sum, &c. 
1866 Twice the sum, &c. 



6691 Sum total. 










100 The common 


distance. 




3)669 


100 








223033 The area 


of the figure A C D G. 


frapezo 


id C E F D. 




Triangle 


EBF 


97 






67 




44 






44 




141 






268 




100 






268 




14100 






2948 





Double areas. 
14100 Trapezoid CE F D 
2948 Triangle EBF. 



2)17048 Sum. 

8524 The area of the figure CBD. 
223033 Ditto of the figure ACDG. 
2.31557 Sum. 

4 

1.26228 
40 



10 49120 



Hence the area of the ^hole figure A C E B F D G A, i* 
2a. Ir. IO^p. nearly. 



Part III.) LAND-SURVEYING. 101 

2. Lay down a piece of ground, and find its area from the 
following equidistant ordinates. 





AB 





1000 


85 


900 


150 


800 


200 


700 


230 


600 


247 


500 


250 


400 


240 


300 


216 


200 


180 


100 


130 


000 


egin 


at A, and 





75 

125 

160 

180 

185 

177 

157 

125 

73 






102 land-surveying. (Part III. 



The first and last ordinates. 

130 The first ordinate. 
000 The last ditto. 
130 Sum. 



The even ordinates. 
180 + 73 — 253 Second. 
240 + 157 = 397 Fourth. 
247 + 185 = 432 Sixth. 
200 + 160 = 360 Eighth. 
85 -f 75 = 160 Tenth. 

1602 Sum. 
4 



6408 Four times the sum. 



The odd ordinates. 

216 + 125 = 341 Third. 
250 + 177 = 427 Fifth. 
230 + 180 = 410 Seventh. 
150 + 125 = 275 Ninth. 

1453 Sum. 
2 



2906 Twice the sum. 



130 The first and last ordinates. 
6408 Four times the sum, &e. 
2906 Twice the sum, &c. 
9444 Sum total. 

100 The common distance. 
3)944400 
3.14800 Area in square links. 



.59200 
40 

23.68000 Area 3a. Or. 23 |p. 



3. Required the plan and area of a piece of ground, from the 
following equidistant ordinates. N 



Part III.) 



LAND-SURVEYING, 



103 





AB 


220 


1200 


234 


1100 


245 


1000 


250 


900 


246 


800 


235 


700 


221 


600 


200 


500 


176 


400 


140 


30® 


100 


200 


55 


100 





000 


-gin 


at A, and 



range E. 



Answer. 

220 The first and last ordinates. 
4456 Four times the sum, &c. 
1976 Twice the sum, &c. 
6652 Sum total. 

100 the common distance. 
3)665200 

2.21733 Area in square links. 
4 

.86932 
40 

34.77280 Area 2a. Or. 34|p. 



4. Find the area of 4 lands, measured by equidistant ordi- 
nates, from the following notes. 



182 


1290 


183 


1200 


178 


1100 


189 


1000 


190 


900 


187 


800 


179 


700 


150 


600 


182 


500 


185 


400 


180 


300 


160 


200 


170 


100 


188 


000 




... .. 



70 

101 

115 

112 

96 

98 

95 

100 

120 

110 

131 

133 

137 

130 



H 4 



104 



Land- ; vzyixg. Part 111, 

602 The first and last ordin i 
. Four times the sum, &c. 



: 5am total. 

100 The common distance. 

— -— 

I rapeaoid at the end. 
3." : . Area in square li: 



c :■:: — 
*o 

c.-i :■ 



Area 3a. 3b. Of p. 



5. Find the area oi 
*■: Hiving iizifzsiiz.;. 



5, by equidistant ordinates, from the 



14? 


c r 


153 


?■:■:■■• 


- 


:-•:■■:■ 


: : : 


•:,: :< 


14-9 


•: : : ■- 


14*3 


is-: o 


144 


i t : :• 


142 


-.::• 




t-00 


I4fl 


fOfl 


141 


GOO 


145 


• : :■ 



A:- ":: 

298 The first and last ordinates. 
2936 Four times the sum. & : 
1171 T^ice the sum. ft : 
4408 Sam total. 



S :?.-4 " 



4 " x : 

DO Trapexoid at the end. 

1 r Area in square 0. 

4 



2.172 



6.88000 Area. 4a. 2k. 6f p. 



Part III.) LAND-SURVEYING. 105 

6. Required the plan and area of a piece of ground from the 
following equidistant ordinates. 



180 

220 

246 

265 

270 

269 

260 

243 

215 

180 

134 

65 



goW. 

Answer. 
743 The first and last ordinates. 
7900 Four times the sum, &c. 
3264 Twice the sum, &c. 

Tl907 Sum total. 

100 The common distance. 





AB 


236 


1200 


170 


1100 


126 


1000 


90 


900 


67 


800 


55 


700 


57 


600 


66 


500 


87 


400 


120 


300 


170 


200 


232 


100 


327 


000 


Begin 


at A, and 



3)1190700 

3.96900 Area in square links. 
4 



3.87600 
40 

35.04000 



Area 3a. 3r. 35p. 



7. Required the plan and area of a field from the following 
equidistant ordinates. 





AB 


217 


1096 


187 


1000 


150 


900 


125 


800 


107 


700 


98 


600 


95 


500 


100 


400 


114 


300 


130 


200 


167 


100 


190 


000 


Begin 


«.t A, and 



202 

150 

112 

84 

66 

58 

57 

65 

80 

110 

148 

200 

go X. 



106 land-surveying. (Part III, 



Answer. 

727 The first and last ordinates. 
4384 Four times the sum, &c. 
1540 Twice the sum, &c. 

6651 Sum total. 

100 The common distance. 

3)665100 

221700 
36288 Trapezoid at the end. 

2.57988 Area in square links. 
4 

2^31952 
40 



12.78080 Area 2a. 2r. 12|p. 



Note. — Whenever the rule given in this Problem can be applied, it will 
be found more easy, expeditious, and accurate, in finding the areas of offsets, 
and of narrow pieces of land, than the rules for triangles and trapezoids. 
(See my Mensuration, page 274.) 



Part IILj LAND-SURVEYING. 



107 



PROBLEM X. 
TO FIND THE BREADTH OF A RIVER. 

EXAMPLE. 

Let the following figure represent a river, the breadth of 
which is required. 

B 




Fix upon any object B, close by the edge of the river, on the 
side opposite to which you stand. By the help of your cross, 
make A D perpendicular to A B ; also make A C = C D, and 
erect the perpendicular D E ; and when you have arrived at the 
point E, in a direct line with C B, the distance D E will be = 
A B, the breadth of the river ; for by Theo. 1, Part I, the angle 
A C B = D C E, and as A C = C D, and the angles A and D 
right angles, it is evident that the triangles A B C, C D E are 
not only similar but equal. 



Note 1. — The distance between A and the edge of the river, must be de- 
duced from D E, when it is not convenient to fix A close by the river's edge. 

2. — This Problem may also be well applied in measuring the distance of 
any inaccessible object ; for let A C equal 8, C D equal 2, and D E equal 10 
chains ; then, by similar triangles, as CD :DE : : A C : A B ; that is, as 
2 : 10 :: 8 : 40 chains = A B. (Sec Thco. 11, Part I.) 



108 



LAND-SURVEYING. (Part III. 



PROBLEM XI. 

LINES UPON WHICH THERE ARE IMPEDIMENTS 
NOT OBSTRUCTING THE SIGHT. 



EXAMPLE. 



Suppose m n, to represent a deep pit or water, and A and B 
two objects, the direct distance of which is required. 
At the verge of the 



impediment, having 
fixed the mark m, in 
a right line with A 
and B ; measure from 
A to m ; and at m, 
by the help of your 
cross, erect the per- 
pendicular m a, which 
measure to the out- 
side of the interposed 
obstruction, as at c. 
Then on the other 
side, as at n, in a 
line with A and B, 
erect the perpendicu- 
lar n e ; and make n b 
equal to m c. 

Measure b c, which 
will be equal to m n ; 
and from n, measure 
the distance n B ; then 
b c, added to A m 
and n B, will give the 
whole distance A B, 



9B 




4A 



Part III.) LAND-SURVEYING. 



109 



PROBLEM XII. 

LINES UPON WHICH THERE ARE IMPEDIMENTS 
OBSTRUCTING THE SIGHT 



EXAMPLE. 

Suppose C D E F to represent the base of a building, which 
obstructs the sight, and through which it is necessary that a 
straight line should pass from an object at A, 

Measure from A to 
m ; at m, erect the 
perpendicular m a, 
which measure until 
you are clear of the 
impediment, as at c, 

Erect the perpen- 
dicular c e, which 
measure until you are 
beyond the building, 
as at b. Erect the 
perpendicular b d ; 
and make b n, equal 
to m c, at which 
point you will be in a 
direct line with m A. 
Erect the perpendi- 
cular n B, which mea- 
sure ; then b c, added 
to A m and n B, will 
give the whole dis- 
tance A B. 

Note. — The last two pro- 
blems are very useful when 
you meet with impediments 
upon a base-line> 




LAND-SURVEYING. 



^art tijt tfouvfy. 

The Method of Surveying with the Chain only ; and 
of measuring Meres. Woods, Distances, Lines upon 
which there are Impediments, and Hilly Ground. 



MISCKLLANEO US INSTE UCTIQN& 

JL he method of surveying with the chain only, is adopted by 
most Practical Surveyors, and is certainly preferable to that by 
the chain and cross ; because it is not only always as accurate, 
but generally more expeditious. 

TThatever be the form of the field or ground to be surveyed, 
you must measure as many lines as will enable you to plot it 
with accuracy. The plan being drawn, you may then divide 
the figure into trapeziums, triangles, kc; and measure the 
diagonals, perpendiculars. &e. with your plotting-scale. 

It is better, however, to divide small pieces, and single fields, 
into trapeziums and triangles, by measuring the diagonals and 
daring the survey ; so that to find the area, you will have 
only the perpendiculars to measure with the scale. 

You must also measure, in some convenient direction, a 
proof-line to each trapezium and triangle. 

Ni :-: 1 . — The offsets must be treated according to the directions in Part III. 
Prob. 6. Or, you may reduce the crooked sides to straight ones, by including 
as much of what does not belong to the field under your survey, as you ex- 
clude of what does, in the following manner. Apply to the crooked line in 



Part IF.) LAND-SURVEYING. Ill 

question, the straight edge of a clear piece of lantern horn, so that the small 
parts cut off by it, from the crooked figure, may be equal to those which are 
taken in ; (of this equality you will presently be able to judge very cor- 
rectly, by a little practice ;) then, with a pencil, draw a line by the edge of 
the horn. The sides being thus successively straightened, the content may 
be easily found. 

2. — A slender bow of cane or whale-bone, strung with a silk thread, may- 
be substituted for the horn. The thread must be applied to the crooked 
fence, and two marks made, by which a straight line must be drawn. 

3. — The sides may also be straightened by a parallel ruler ; but the 
operation is generally tedious, and must be performed with the greatest 
care, or it will not be more correct than the foregoing method. 

4. — When the three sides of a triangle are given, the area may be found 
as follows. From half the sum of the three sides subtract each side seve- 
rally ; multiply the half sum and the three remainders continually together, 
and the square root of the last product will be the area required. This 
method is too prolix, except in particular cases ; the operation may, how- 
ever, be considerably simplified, by performing the multiplication and evo- 
lution by Logarithms. 



PROBLEM I. 

TRIANGULAR FIELDS. 

When you have a triangular field to survey, begin at the 
most convenient corner, and measure each side ; and, while 
measuring any one of the sides, leave a mark in some situation 
on the chain-line, that the distance between it and the opposite 
angle being measured, may be a proof line. 

Or, leave marks upon any two of the chain-lines, and the 
distance between them will prove your work. 

EXAMPLES. 

1. It is required to construct a figure, and find its area, from 
the following notes. 



112 



LAXD-SLRVEY1XG, 



(Part IK. 



DC 

913 proof-line. 

Return to D. 



Begin at 




D, station for a proof-line. 




Having constructed the figure, you will find the line D C to 
measure 913 links, as in the field-book ; hence, you may con- 
clude there is no error committed in taking, or setting down 
the dimensions. 

Note 1 . — If your proof-line upon the plan does not agree, or nearly so, 
with that taken in the field, you may be assured that some error has been 
committed ; you must, therefore, repeat the survey in order to discover it. 



2. — When land is level, and the lines are well driven, and not very long, 
you will generally find them to meet correctly, 



Part IV.) LAND-SURVEYING. 113 

TO FIND THE PERPENDICULAR. 

Vide Part I. Prob. 6. 
Or, if you make use of a plotting-scale, lay it across the base 
in such a manner, that the line which goes across the scale 
may coincide with it, the edge of the scale at the same time 
touching the opposite angle ; by that edge draw a line from 
the base to the opposite angle ; this line, or perpendicular C a, 
in the present case, you will find to be 878 links. 

1462 base. 
878 per. 

11696 
10234 

11696 

2) 1283 636 

6.41818 
4 

1.67272 
40 



26.90880 Area 6a. 1r. 27p. 



COMPUTATION OF THE AREA FROM THE THREE SIDES. 

TT 1462 + 1275-1-1029 3766 n _ „,._ 

Here — = — — = 1 883, half the sum of the 

2 2 

three sides. Then 1883 - 1462 = 421, the first remainder; 

1883 - 1275 = 608, the second remainder; and 1883 - 1029 = 



854, the third remainder ; whence -v/1883 X 421 X 608 X 854 = 
^41161 7533376 = 641574 square links, the area, equal to 6 
acres, 1 rood, and 26^ perches, nearly the same as before. 



THE SAME BY LOGARITHMS. 

The log. of 1883 = 3.2748503 

421 = 2.6242821 

608 = 2.7839036 

854 = 2.931 4579 

Divide by the index of the root 2 )1~1. 6144939 

The quotient is the log. of 641 574, the area ~~ 5.8072469 



Ill 



land-surveying. 



rPart IV. 



2. It is required to construct a figure, and find its area, from 

'.lowing n 





C A 


o 




- 








U 


- 


yg 




15 




55 


212 




) 




R. [ 




B C 






4 




M 


354 




22S 








: >ffB. 




AB 


Q 





a proof-line, 
which goes to n, and 
measures 352 links. 



48 

V 
56 

2 5 



745 



:ion for a proof -line. 



Begin at A. Range N. E. 



computation or the aw fpsbts, &c 

B 




Part IF.) LAND-SURVEYING. 115 

Having constructed the figure, you will find the line m n to 
measure 352 links, as in the field-book. You will also find the 
perpendicular B a, to be 528 links. 

Triangle ABC. 

1252 base. 
528 per. 

10016 

2504 
6260 
661056 



256 
25 

1280 
512 

6400 

25 

56 

81 
239 

729 
243 
162 

19359 



Offsets taken on the line A B. 

56 

76 

132 

105 

660 
132 

13860 



76 

48 

124 

145 

620 
496 
124 

17980 



228 




48 




1824 




912 




10944 




~64(Xn 


! 


19359 | 


1 Double 


13860 


> areas 


17980 | 


collected, 


10944 


i 


68543 i 


mm. 








12 



]16 



LAND-SURVEYING. 



(Part IV. 



229 
49 




49 
64 

113 
125 

505 
226 
113 

14125 



Offsets taken on the line B C. 

64 
4U 

104 

182 

208 

S32 
104 



I S 9 2 > 

147 
_ *° 




Double 

areas 

collected. 



50154 sum. 



Offsets taken on the line C A, 



232 


72 


252 


55 


45 


37 


1060 


117 


1764 


LC 


106 


756 


11660 


7 "2 


9324 


55 


11, 
12402 


11660" 




15 




14840 






45 
69 


16182 


Double 


,0 


12402 


\- areas 


212 


12312 


collected 


14840 


114 


18656 






108 


9324 v 








15 


912 


95376 sum. 


72 


114 











87 
186 

522 


12312 




69 




696 


37 




87 


106 




16182 


176 






636 
742 
106 






18656 







Part IV,) LAND-SURVEYING. 



661056^ 
68543 ( 



Whole 
50154 ^ double areas 
05376 j collected - 



2)875129 

4.37564 
4 

1750256 
40 

20.10240 Area 4a. 1r. 20e. 



117 



COMPUTATION OF THE AREA BY REDUCING THE CROOKED SIDES 
TO STRAIGHT ONES : GENERALLY CALLED " CASTING." 

JB 




Having constructed the figure as before, and taken out the 
chain-lines ; draw the three dotted lines A B, B C, and C A, 
in such a manner, that the parts included may be equal to those 
excluded, as nearly as your eye can judge. Then the base A O 
being measured, will be found = 1390 links; and the perpen- 
dicular B a = 630 links. 

1390 base. 
630 per. 

41700 
8340 



E 



2)875700 

4.37850 

4 

1.51400 

40 
20.56 000 Area 4a. Ir. 20p. 

i 3 



118 



LAND-SURVEYING. 



(Part IV. 



Note. — Although the method of finding the area by Casting (which de- 
pends entirely upon the accuracy of the eye) is adopted by most Practical 
Surveyors ; it is certainly less correct than that by Offsets, &c. A learner, 
therefore, ought to practice both, until he can habitually come very near 
to the truth by the former. 

3. Lay dov\Ti a field, and find its area, from the following 
notes. 








BD 




760 


Return 


to 




DA 




1035 




R. offD. 









CD 


61 


1145 


55 


1100 


12 


1000 


72 


950 


119 


900 


80 


850 


61 


800 


59 


750 


110 


700 


179 


600 


210 


550 


215 


500 


212 


450 


180 


400 


159 


350 


142 


300 


165 


250 


173 


200 


161 


150 


126 


100 


65 


50 





000 




R. offC. 




A~C 




1590 


B 


890 


Begin at 


A, and 







proof-line. 
B. 



Range AV 



Part IV.) LAND-SURVEYING. 



119 



Answer. 
Having constructed the figure, you will find the perpendicular 
D a, upon the base A C, to measure 740 links. 
Double areas. 

1176600 Triangle A C D. 
275770 Offsets taken on the line C D. 
Area 7a. 1r. If p. 

4. Lay down a field, and find its area, from the following 
dimensions. 





D B 






575 


proof-line. 


Return 


to 


D. 




C A 






1320 




D 


600 
R. off C. 






BC 







880 




31 


800 




73 


750 




95 


700 




58 


600 




60 


550 




95 


500 




60 


380 




63 


250 




60 


200 




45 


100 




55 


000 
R. off B. 




To 


the 


fence. 


30 


930 




17 


875 


to B. 


48 


800 




65 


700 




74 


600 




65 


500 




58 


400 




55 


300 




30 


200 




17 


100 







000 




Begin 


at A, and 


Range N. 1 



I 4 



120 



LAND-SURVEYING. 



(Part IV. 



Answer. 
Having constructed the figure, you will find the perpen- 
dicular B a, upon the base A C, to measure 573 links. 

Double areas. 
756360 Triangle ABC. 

85060 Offsets taken on the line A B. 
106270 Ditto on the line B C. 

Area 4a. 2r. 38p. 

5. Lay down a field, and find its area, from the following 
notes. 





DC 




596 


Return 


to 




C A 




1080 


6 


1000 


50 


900 


110 


800 


130 


700 


145 


620 


106 


550- 


65 


500 


30 


450 


16 


410 


36 


350 


54 


300 


70 


250 


74 


200 


86 


150 


70 


100 


46 


50 


O 


000 




K, off C. 



proof-line. 
D. 



D, station for 
a proof-line. 



Part IV.) LAND-SURVEYING. 



121 



"8 

J 

C 

GO 

M 

P 



© 

M 

o 
o 

A 










BC 





848 


30 


800 


60 


750 


80 


700 


70 


650 


48 


600 


20 


520 


46 


450 


90 


380 


100 


330 


110 


270 


70 


200 


40 


150 


50 


100 


45 


000 




R. off B. 


To 


the fence. 


50 


800 


45 


755 


30 


700 


40 


650 


# 75 


600 


130 


550 


170 


500 


156 


450 


135 


400 


50 


350 


24 


300 


66 


250 


80 


200 


40 


150 


20 


100 


23 


50 





000 


From 


A, Range 



toB. 



N. E. 



Answer. 
Having laid down the figure, you will find the perpendicular 
B a, upon the base A C, to measure 587 links. 
Double areas. 
633960 Triangle ABC. 
110800 Offsets taken on the line A B. 
100120 Ditto on the line B C. 
149310 Ditto on the line C A. 
Area 4a. 3r. 35|p. 



122 land-surveying. (Part IV. 

PROBLEM II. 
FIELDS IN THE FORM OF A TRAPEZIUM. 

When you have a trapezium to survey, measure each side, 
and both the diagonals, one of which will enable you to con- 
struct the figure, and the other will serve as a proof-line : or, 
you may measure the longer diagonal, and a proof-line in any 
other direction most convenient. 

Note I. — From various obstructions it is sometimes impossible to take 
either of the diagonals ; in such cases, you must measure tie-lines across 
the angles of the field, at any convenient distance (not less than two chains) 
from the corners. These you will find sufficient for constructing the figure, 
and for proofs. Or, you may take an external angle, or angles, as directed 
in Problem IV. 

2. — When the lines, including the angle you intend to take with the chain, 
are of a considerable length, it vail be necessary to measure more than two 
chains from the angular point, before you take the chord-line ; because a small 
inaccuracy in constructing the figure, when the angular distance is short, will 
throw the lines, when far produced, considerably out of their true position. It 
sometimes happens, however, in consequence of obstructions, that it is im- 
possible to measure the chord-line at a greater distance from the angular 
point, than one or two chains. In such cases, multiply both the chord-line and 
angular distance by 2, 3, 4, or any larger number, as circumstances may 
require ; and use the products resulting, in laying down the figure. 

3. — When the measurement of the surface is required,for reaping, &c. you 
must let the chain touch the sides of the lands, in all places where you measure 
across them. If you do not measure across the lands, but along the headland ; 
then you must add as many links to the length of the chain-line, as will make 
it equal to one measured across the lands, parallel to and near the headland. 

You may easily ascertain what number of links you oUght to add, by stretch- 
ing the chain across the lands, and putting down an arrow at each end ; after 
which, leave hold of one of the ends, and you will observe it recede from the 
arrow. The number of links, by which it falls short of its former position, 
you must add to each chain. Some lands you will find so low, that nothing 
need be added to the chain-line ; and some will require a link to four, three, 
two, or even (where the lands are very high) a link or more to one chain. 

To this method some may object ; but, when the lands are high, if the lines 
measured along the headlands be not lengthened, the perpendiculars will 
obviously measure less than they ought to do ; consequently, the horizontal 
measure will be returned, instead of the measure of the surface. 



Part IV.) LAND-SURVEYING. 123 

In the opinion of others, the diagonal, measured with a slack chain, will 
give the measure of the surface ; but, in this case, the perpendiculars will 
evidently he shorter than they would have been, if the diagonal had been 
measured with a tense chain ; consequently, the measurement will be the 
same, or very nearly the same, whether the diagonal be measured with a 
tense or slack chain, unless the headland lines be lengthened. 

4. — If two or three persons measure the same piece of land separately, or 
even if one person measure the same piece twice over, there will generally 
be a difference between the measurements ; this difference, however, in 
small pieces, should scarcely ever exceed four or five perches. 

5. — When land, crops of corn, &c. are bought and sold, the buyer and 
seller commonly choose each a surveyor ; and in their measurements it oc- 
casionally happens that there exists a considerable difference. In this case, 
the best method, perhaps, of adjusting the dispute is, that the two surveyors 
meet, and jointly remeasure the land. If this fail, it only remains that the 
buyer and seller jointly choose an experienced surveyor, as an umpire, by 
whose decision the law will compel the parties to abide. 



EXAMPLES. 

1 . It is required to construct a figure, and find its area, from 
the following notes. 



Begin at 



BD 




1400 
1000 


Diag. 


Return 


toB. 


AC 




1916 

1000 


Diag. 


R. off A. 




D A 




558 




R. offD. 




C~D 




1626 




1000 




R. off C. 




BC" 




689 




R. off B. 









AB 




1492 




1000 




A. Range 


W. 



124 



LAND-SURVEYING. (Part IF. 

_ x> 




Having constructed the figure, lay your scale from B to D; 
and if you find it exactly 1 400 links, as in the field-hook ; you 
may then measure the perpendicular B a = 468 links ; and the 
perpendicular D a = 432 links ; from which you will readily 
compute the area required. 



468 
432 



per. 



900 sum. 
1916 diag. 

2)l724400 

8.62200 
4 



2.48800 
40 



19.52000 . Area 8a. 2r. 19p. 



BY THE FALSE METHOD. 



Remarked in Part III. Prob. 4. Note 4. 



1492 =AB 
1626 = C D 


1559 
623 


2)3118 

1559 mean length. 


4677 
3118 
9354 


689 = B C 
558 = D A 

2)1247 

623 mean breadth. 


9.71257 
4 

2.85028 
40 

34.01120 



Here the area is found to he 9a. 2r. 34p., which is too much 
by 1a. Or. 15p. ; but the more nearly a trapezium approaches 
to a square, or rectangle, the less will be the error. 



Part IV.) LAND-SURVEYING. 125 

2. Required the area of a field, from the following notes. 



Begin at 



DB 




1365 


Diag. 


1000 




Return 


toD. 


AC 




1288 


Diag. 


1000 




L. off A. 




DA 




750 




L. off D. 




CD 




765 




L. offC. 




BC 




720 




L. off B. 




AB 




1600 




1000 




A. Range 


E. 




Having constructed the figure, you will find that in conse- 
quence of the length of the side A B, a perpendicular from the 
angle A to the diagonal D B, cannot be taken; you must, 



126 LAND-SURVEYING. (Part IV. 

therefore, let fall the perpendicular D a, from the angle D to 
the side A B, which you will rind = 638 links. The perpen- 
dicular C a will be found = 294 links. 

> 



Triangle A B D. 
1600 base. 
638 per. 

12800 

48 
96 


Triangle B C D 
1365 base. 
294 per. 
5460 

12285 

2720 


1020800 


401310 


1020800 | 

401310 J 


Double areas, 
collected. 


2)1422110 




7.11055 
4 




.44220 
40 




17.68800 


Area 7a. 0itri8p. 



3. It is required to find the area of a field, from the following 
notes. 





B D 




1236 




1000 




Return to B. ; 




AC 




1326 




1000 




R. off A. 




D A 





515 


28 


400 


50 


300 


65 


200 


33 


100 





000 




R. offD. 



Diag. 



Diag. 



Part IV.) LAND-SURVEYING. 



127 










CD 





1375 


50 


1300 


7a 


1200 


84 


1000 


52 


800 





652 





356 


44 


200 


50 


100 





000 




R. off C. 




BC 





664 


25 


570 





483 





378 


32 


300 


72 


150 


85 


100 


60 


50 





000 




R. off. B. 




AB 




946 





784 


50 


725 


93 


650 


106 


600 


75 


500 


32 


400 





335 





242 


50 


40 





000 


Begin at 


A. Range 



E 



128 



LAND-SURVEYING. Part IV.) 



BY OFFSETS, &C. 




Having constructed the figure, you wffl find the perpen- 
dicular D a = 512, and the perpendicular B a = 446 links. 



Trapezoid A B C D. 

is}** 

958 sum. 
1326 diag. 

5748 
1916 

2874 
958 



1270308 



Part IV.) LAND-SURVEYING. 



129 



Offsets taken on the line A B. 



242 


75 




59 


50 


106 


50 


12100 


181 

100 


2950 






65 


18100 




32 


=— 


12100' 




130 


106 


2080 




195 


93 • 


10700 


Double 


2080 


199 


18100 )■ areas 




50 


9950 


collected 


32 

75 


9950 


10725 
2950^ 




107 
100 


93 


66605 Sum. 


50 




10700 


143 

75 










715 






1001 






10725 






■ 







50 
60 

3000 



60 
85 

145 
50 

7250 

85 

72 

157 
__50 

7850 



Offsets taken on the line B C. 

72 
32 

104 
150 



5200 
104 

15600 



78 
__32 

156 
234 

2496 



181 

25 

905 
362 

4525 



3000 
7250. 
7850 f Double 
15600 r ™ e ™ a 
2496 V collected. 

4525 



40721 S um . 



130 



LAND-SURVEYING. (Part IV. 



100 
50 

5000 

50 
44 

94 

100 
9400 

156 
44 

624 

624_ 

6864 

148 

52 

296 
740 
7696 



Offsets taken on the line C I>, 

52 

84 

136 

200 



27200 

84 
75 

159 
200 

31800 

75 
50 

125 
100 

12500 

75 

_50 
3750 



5000] 




9400 




6864 


Double 


7695 ] 


[■ areas 


27200 


collected 


31800 




12500 




3750 J 




104210 Sura, 



Offsets taken on the line D A. 



33 


50 


100 


28 


3300 


78 


ZZZ.ZZZ 


100 


33 
65 


7800 


98 


115 


ioa 


28 


9800 


£20 




230 




65 


3220 


50 


: — : — 


115 




100 




11500 





3300^ 

9800 / Double 
11500 > areas 

7800 I collected. 

3220.) 
35620 Sum. 



Part IV.) LAND-SURVEYING. 



131 



Whole 

-double area* 

collected. 



1270308 

66605 

40721 

104210 

35620 

2) 1517464 

7.58732 
4 

2.34928 
40 

13.97120 Area 7a. 2r. 14p. 



BY CASTING. 




Having constructed the figure, draw the four dotted lines 
A B, B C, C D, and D A, in such a manner, that the parts in- 
cluded may be equal to those excluded ; then the diagonal A C, 
will be found = 1364, and the perpendiculars Da = 636, and 
Ba = 476 links. 



k2 



182 



LAND-SURVEYING, 



(Part IF. 



636 
476 



per. 



1112 sum. 
1364 diag, 
4448 
6672 
3336 
1112 



2) 1516768 
7.58384 

4 

2.33536 
40 

13.41440 Area 7a. 2r. 13p. 



4. It is required to find the area of a field, from the following 
notes, 



BD 




1460 


Dif 


1000 




Return to B. 




AC 




1480 


Dh 


1000 




R. off A. 




DA 




672 




R. off D. 




CD 




1244 





1000 


47 


800 


70 


600 


85 


400 


68 


200 


30 


000 





r. off c. 





Part IV.) LAND-SURVEYING, 



133 





BC 







720 




85 


650 




112 


550 




88 


450 






360 


Cross the fence. 




300 


83 




200 


130 




100 


100 




000 







R, off B, 






AB 






1350 






1000 




n at 


A. Range 


W, 



c 




*> 




Having constructed the figure, you will find the perpen- 
dicular C a = 613, and the perpendicular A a = 618 links. 
Trapezium A B C D. 

613) 
_618|P er - 

1231 sum. 
1460 diag. 

73860 
4924 
1231 



1797260 



k3 



134 



LAND-SURVEYING^. (Part IV. 



Insets taken on the line B C. 




100 
130 

230 
100 

23000 



130 
83 

213 
100 

21300 

83 
60 

4980 



10000) 

23000 (Double areas 

21300 ( collected. 

4980J 
59280 Sum. 



Offsets taken on the line B C. 



88 
90 

7920 


112 

85 

197 
100 

19700 

85 
70 

5950 

Insets taken 

85 
70 

155 
200 

31000 

70 
47 

117 
200 

23400 


7920^) 
20000 (Double areas 
19700 ( collected. 

5950 J 


88 


53570 Sum. 


112 

200 
100 

20000 




200 
30 

6000 

30 
68 

~~98 


on the line C D. 

6000 \ 
19600/ 

30600 { Double areas 
31000 ( collected. 
23400 \ 
11468 J 

122068 Sum. 


200 
19600 




68 
85 




153 
200 


244 
47 




30600 


3708 

976 

11468 









Part IV.) LAND-SURVEYING. 

Double areas. 

1797260 Trapezium ABCD. 

53570 Offsets. 
1850830 Sum. 

~ 59280 
122068 



135 



Insets. 



181348 Sum to be deducted from the above sum. 
2)1669482 Whole field. 

8.34741 

4 



1.38964 
4t) 



15.58560 Area 8a. 1r. 16p. 



5. It is required to find the area of a field, from the^following 
notes; neither of the diagonals having been measured, in con- 
sequence of obstructions. 



Begin at 



DA 




476 




L. offD. 




CD 




618 




200 


r, proof-line, 417 to B. 


L. offC. 




BC 




443 




L. offB. 




AB 




723 




192 


from m to n. 


200 


from A to m, on the line A D< 


200 


from A to n, on the line A B. 


the angle 


A range E. 



K4 



136 



LAND-SURVEYING. 
D 



(Part IV. 




fr..-": 




Having constructed the figure, you will find the diagonal 
AC = 963, and the perpendiculars Da = 257, and B a = 316 
links. 

573 sum. 
963 diag. 

1719 
3438 
5157 
2)551799 

2.75899 
4 

3.03596 
40 
1.43840 Area 2a. 3r. Ip. 



Part IF.) LAND-SURVEYING. 



137 



6. Required the plan and area of a field, from the following 
notes. 





BD 

1437 

1000 

Return to B. 




AC 

939 
L. off A. 




D A 

567 
L. offD. 




CD 

712 
L. offC. 




BC 

765 
L. offB. 


Begin at 


AB 

1457 

1000 

A. Range 



Diag. 



! Diag. 



E. 



Answer. 

Having constructed the figure, you will find one of the per- 
pendiculars = 560, and the other = 166 links; hence the area 
is = 5a. Or. 34p. 



7. It is required to lay clown a field, and find its area, from 
the following notes. 






Pari IV* 



B D 

_ 






t 7 _;_ 



DA 

l - d 



: 

1 :z '. 



L. :f I 



A B 
2 

^ •: :■ 
; ; 

A. Range 






---"- = 





E. 



Answer. 

ii-il-irs = Li: = -IS '__ £i : i.-_.t :lr m 

Li = 



- " required to lay down a field, and find its area, from 
tike following notes; neither of the diagonals haying been 



B 




-.'-':'. 




:.:•■: 




L - 








Part IV.) LAND-SURVEYING. 



139 



Begin at 



AC 

1094 
L. off A. 



E A 

1800 

1000 

L. offE. 



DE 

837 
L. off D. 



BD 

1528 
1000 
860 
L. off B. 



A B 

621 
A. Range 



N. 



Answer. 

Having constructed the figure, you will find the diagonal 
BE = 1927, and the perpendiculars = 580 and 637 links re- 
spectively ; hence the area is = 11 a. 2r. 36p. 



9. The plan and area of a field are required from the fol- 
lowing dimensions. 



Return 



DB 

1730 
toD. 



AC 

1660 
R. off A. 



Diag. 



Diag. 



140 



LAND-SURVEYING. 



(Part IV. 



To 


the 


Fence 


99 


1580 




110 


1500 


to A. 


100 


1450 




116 


1400 




132 


1300 




115 


1200 




65 


1100 




33 


1000 




25 


950 




40 


900 




150 


850 




210 


800 




250 


700 




255 


630 




240 


550 




218 


500 




117 


400 




41 


300 




18 


250 




15 


200 




100 


150 




140 


100 




157 


50 




165 


000 
R. offD. 




To 


the 


Fence. 


60 


1085 




82 


920 


toD. 


80 


850 




42 


750 




40 


700 




121 


600 




140 


550 




136 


500 




70 


400 




25 1 


350 




17 j 


300 




14 


250 




30 ! 


200 




70 


150 




92 1 


100 




100 


000 
R. offC. 








Part IV.) LAND-SURVEYING, 



141 



To 


the 


Fence 


52 


1440 




70 


1340 


toC. 


60 


1250 




37 


1200 




33 


1150 




45 


1100 




83 


1000 




70 


900 




25 


800 




12 


750 




20 


700 




40 


650 




48 


600 




54 


500 




59 


450 




60 


400 




72 


350 




84 


300 




70 


200 




86 


150 




80 


100 




75 


000 
R. off B. 










To 


the 


Fenc< 


67 


1005 




78 


930 


toB. 


86 


850 




90 


750 




75 


700 




40 


650 




27 


600 




36 


550 




57 


500 




85 


450 




78 


400 




58 


300 




62 


200 




79 


100 




83 


50 




80 


000 




legin 


at A, and 


goN 



Answer. 



Having constructed the figure, you will find the pern 
diculars A a = 810, and Car 708 links. 



142 



LAND-SURVEYING. 

Double ar 

2626140 Trapezium A B C D. 
13794.5 Offsets taken on the line 
167800 Ditto on the line B C. 
1.57520 Ditto on the line C D. 
39.5420 Ditto on the line D A. 



(Part IV. 



A B. 



3484825 Sara. 



Area 17a 1r. 27^ p. 



PROBLEM III. 



FIELDS OF MORE THAX FOUR SIDE>. 

TVhen a field consists of more than four sides, you rnusr 
divide it into triangles and trapeziums, agreeably to the direc- 
tions given in Part III. Prob. 5. Then take the dimensions 
of each, as directed in the last two problems. 



Note. — Notwithstanding what has already been advanced with regard to 
taking proof- lines, you are again requested never_to omit measuring such 
distances as will enable you to confirm every part of your survey. Some may 
perhaps deem this tedious and superfluous ; but the satisfaction which a Sur- 
veyor finds, when his lines meet correctly, fully compensates him for his ad- 
ditional labour. Beside, he had certainly much better be at the pains of de- 
tecting his own errors, than expose himself to ridicule, by suffering them to 
be detected by some other Surveyor. 



EXAMPLES. 



1. It is required to find the area of a field, from the following 
notes. 



Diag. 




Diag. 

m, proof-line, goes to D, 
and measures 285. 



Part IV.) LAND-SURVEYING 



143 



Begin at 



AC 

1200 

1000 

R. off A. 



E A 

393 
R. off E. 



DE 

692 
R, off D. 



CD 

620 
R. off C. 



BC 

535 
R, off B. 



AB 

1334 

1000 

A. Range 



Diag. 



W. 




Having constructed the figure, you will find the perpen- 
diculars C a = 410, Aa = 330, and D a = 215 links. 



144 



Trapezium A B C E. 

410) 

330}P er - 

740 sum. 

1510 diag. 



LAND-SURVEYING. (Part IV. 

Triangle C D E. 

1238 base. 
215 per. 



6190 
1238 



7400 


2476 


370 

74 

1117400 


266170 





1117400 ) Double areas 
266 170 J collected. 
2)1383570 

6.91785 

4 

3.67140 
40 



26.85600 Area 6a. 3r. 27p. 



2. It is required to find the area of a field from the follow- 
ing notes, 



DA 

1042 
Return to D. 



CE 

420 
R. off C. 



A C 

768 
Roff A. 



E A 

585 
R. off E. 



DE 

518 
R. offD. 



CD 

365 
L. off C. 



Diag, 



Diag. 



Diag. 



Part IV.) LAND-SURVEYING. 



145 



Begin at 




m, proof-line, goes to C, 
and measures 260. 




Having constructed the figure, you will find the perpen- 
diculars C a = 223, Cn = 200, and E a = 176 links. 



Triangle ABC. 

1054 base. 
223 per. 

3162 
2108 
2108, 

235042 



Trapezium A C D E. 

200) 
176JP er - 

376 sum. 
1042 diag. 

"752 
» 1504 
376 

391792 



146 



LAND-SURVEYING. f Part IV. 

235042 \ Double areas 
391792 / collected. 
2)626834 

303417 

4 

.5366$ 

40 



21.46720 Area 3a. Or. 21p. 



3. It is required to find the area of a field, from the follow- 
ing notes. 



Diag 





FB 




660 




Return to F. 




BE 




970 




L. off B. 




D B 




268 




L. off D. 




AD 




832 




R. off A. 




FA 




285 




L. off F. 




EF 





384 


40 


300 


53 


200 


32 


100 





000 




R. offE. 




D E 








L. offD. 



Diag. 



Diag. 



Diag 



Part IV.) LAND-SURVEYING 



147 





CD 





383 


52 


200 





000 




R. offC. 




BC 




475 




300 




R. off B. 




AB 




850 


Begin at 


A. Range 



m, proof-line, goes to D, 
and measures 255. 



W. 




Haying constructed the figure, you will find the perpendi- 
culars Fa= 185, F m = 185, D n = 190, and D a = 216 
links. 



Triangle A B F. 


Trapezium B D E F 


850 base. 


185 ) 
190/P er ' 


185 per. 


4250 


375 sum. 


6800 


970 diag. 


850 


26250 


157250 


3375 




363750 



L 2 



148 



LAND-SURVEYING 



(Part IV. 



Triangle BCD, 
475 base. 
216 per. 

2850 
475 
950 

102600 



Offset taken on the line C D. 
383 
52 

766 
1915 

19916 



Offsets taken on the line E F- 



32 

100 
3200 

32 
53 

85 
100 

8500 



53 
40 

93 

100 

9300 

84 
40 
3360 



3200 
8500 
9300 
3360 



Double 

areas 

collected. 



24360 sum. 



157250^ 

363750 f Whole 
102600 > double area* 

19916 k collected. 

24360 ) 
2)667876 

3.33938 

4 

E35752 

m 40 
14^30080 Area 3a. 1r. 



14p. 



4. It is required to lay down a field, and find its area, from 
the following notes. 



Part IV.) LAND-SURVEYING, 



149 





DB 

1440 

1000 

Return to D* 




AC 

107S 

L. off A. 

E A~~ 

1324 

1000 

Return to E. 




DF 
712 
L. offD. 




AD 

818 
L. off A. 




FA 

755 
L. off F. 




EF 

692 
L. offE. 




DE 

754 
R. off D. 




CD 

540 
L. off C. 




BC 

1048 
L. off B. 


Begin at 


~AB 

1360 

1000 

A. Range 



Diag. 



Diag. 



Diag. 



Diag. 



Diag, 



L 3 



150 LAND-SURVEYING. (Part IV. 

Answer. 

Having constructed the figure, and divided it into two tra- 
peziums, ABC D, and AD E F : you -will find the perpen- 
dicular -which falls from the angle C upon the diagonal DB = 
31. 5 links; and that which falls from the angle A upon the 
same diagonal = 7-5S links. 

The perpendicular which falls from the angle D upon the 
diagonal E A. you will find = 42.5 links ; and that which falls 
from the angle F upon the same diagonal z=. 28? links. 

Hence the area is = 12a. 1r. 30p. 

5. Required the plan and area of a field, from the following 
notes. 



E B 
424 
R. offE. 


Proof-line. 


F E 

750 
L. ,-r F. 


Diag. 


31 F 

400 

R. offM. 


- 


H M 

R. off H. 


227 to K. 


L H 

R. DffL. 




D L 

43'.' 

Return to D. 




F L 

R. off F. 

H F 

730 

400 

R. off EL 


Diag. 
Diag. 


~~dTT~ 

926 
R. offD. 


Diag. 


GD 
950 
Return to G. 


Diag. 



Part IV.) LAND-SURVEYING. 



151 



Begin at 



GE 

580 
R. off G. 



FG 

630 
R. off F. 



DF 

540 
R. off D. 



AD 

1050 

R. off A. 



E A 

450 
R. off E. 



DE 

670 
R, off D. 



CD 

500 
R. off C. 



AC 

780 

500 

A. Range 



Diag. 



Diag. 



Diag. 



B. 




L4 



152 



LAND-SURVEYING. (Part IV, 



Answer. 

Having constructed the figure, you will find the perpendi- 
culars of the trapezium A C D E = 354 and 195 ; of D F G E 
= 404 and 340 ; ofDLHF = 426 and 316 ; and the per- 
pendicular of the triangle F H M =. 227 links. 

Hence the area of the field is = 10a. 2r. 25p. 



6. Required the plan and area of a field, from the following 
dimensions. 



leturn 


BD 

1480 
toB, 


Diag. 
Line 14 


L. off 


GE 
1725 


Diag. 
Line 13 


L. off 


CG 

1295 

c, 


Diag. 
Line 3 2 


L. off 


FC 

935 


Diag. 
Line 11 


R. off 


DF 

793 
D, 


Diag. 
Line 10 



Part IV.) LAND-SURVEYING. 



153 





GD 





358 


37 


300 


49 


250 


CO 


200 


GG 


150 


62 


100 


30 


50 





000 


R. off 


G, 




FG 





783 


78 


700 


3 34 


650 


154 


600 


170 


550 


172 


500 


150 


450 


185 


400 


208 


350 


205 


300 


180 


250 


149 


200 


107 


150 


62 


100 


24 


50 





000 


R. off 


F, 1 




EF 





1043 


36 


1000 


67 


900 


85 


800 


100 


700 


140 


600 


152 


550 


143 


500 


135 


450 


110 


400 


€5 


350 


50 


300 


40 


200 


25 


100 





000 


R. off 


E, 



Line 9. 



Line 8. 



Line 7. 



154 



LAND-SURVEYING. 



(Part IV. 









CE 





743 


70 


600 


135 


500 


160 


450 


185 


400 


190 


350 


170 


300 


150 


250 


95 


200 


60 


100 





000 


R. off 


o, 




DC 




1000 


L. off 


D, 




AD 




700 




600 




500 




450 




400 




350 




300 




250 




200 




100 




000 


L. off 


A, 




C A 




1578 


R. off 


c, 




BC 





865 


60 


750 


104 


650 


72 


600 


88 


500 


100 


400 


86 


350 


75 


300 


95 


200 


80 


100 


70 


000 


R. off 


B, 



Line 6. 
Diag. 

Line 5. 





50 

130 

160 

173 

184 

190 

150 

107 

60 



Line 4. 



Diag. 
Line 3. 



Line 2. 



Part IV.) LAND-SUItVEYING. 



155 








To 


the 


80 


1820 


73 


1750 


60 


1600 


56 


1500 


70 


1400 


95 


1300 


120 


1200 


105 


1100 


110 


1000 


140 


900 


186 


800 


184 


700 


125 


600 


114 


500 


93 


400 


86 


300 


75 


200 


70 


100 





000 


;gin at 


A, 



Fence. 
toB. 



Range "W. Line 1. 



(See the Figure, Page 39 2. J 

Answer. 

Having constructed the figure, you will find the perpen- 
diculars of the trapezium A B C D, falling upon the diagonal 
C A, to measure 862 and 314 links ; the perpendicular of the 
triangle D G C, falling upon the diagonal C G, to measure 184 
links ; and the perpendiculars of the trapezium CEFG, falling 
upon the diagonal G E, to measure 513 and 300 links. 

Double areas. 



1855728 
238280 

1402425 
362460 
133750 
143250 
149010 
157548 
200374 
30696 

467352? 



Trapezium A B C D. 

Triangle D G C. 

Trapezium CEFG. 

Offsets taken on the line 

Ditto on the line B C. 
> Ditto on the line A D. 

Ditto on the line C E. 

Ditto on the line E F. 

Ditto on the line F G. 

Ditto on the line G D. 
Sum. 



AB, 



Area 23a. Ir. 



18|p. 






LAND-SURVEYING. 



(Pc 



i-i £^i :i-r rr-jT-riTi-f -i- ::' :lr 1 = 7:7:-- ii:'.^-^. it.: :lr 
::---: ::' :if -zi.l-r. ~:~ :1: rill:— Izj Lr_ri^:=5 

—Tie fidd-aotes in tkis example arc entered fin the left to war* 




: :•:-::.- -. 




Part IF.) LAND-SURVEYING. 



157 



1 


ToC 







685 




54 


600 




92 


500 




105 


400 




100 


300 




78 


200 




44 


100 







000 




Go from 


D, 


Line 5. 




ToD 






632 







600 


24 




500 


55 




400 


78 




300 


82 




250 


Gate. 




200 


76 




100 


58 




000 





Go from 


A, 


Line 4. 




To A 






995 


Diag. 


Go from 


c, 


Line 3. 




ToC 







615 




46 


500 




.53 


400 




62 


300 




60 


200 




50 


100 







000 




Go from 


B, 


Line 2. 




""ToT" 







662 




53 


600 




88 


500 




96 


400 




92 


300 




70 


200 




35 


100 







000 




Begin 


at A, 


and go N. Line 1 



158 



LAND-SURVEYING. 



(Part IV. 



To 


the 




668 


ToG 


638 




600 




500 




400 




300 




200 




100 




000 


Go from 


E, 




ToE 




965 


Go from 


D, 




ToD 





735 


32 


700 


75 


600 


55 


500 


20 


430 


Gate 


380 


28 


300 


42 


200 


40 


100 





000 


Go from 


F, 




ToF 




593 




500 




400 




300 




200 




100 




000 


Go from 


E, 




ToE 




712 




600 




500 




400 




340 




274 




200 




100 




000 


Go from 


c, 



Fence. 

22 

24 

26 

42 

48 

45 

30 

18 



Line 10= 



Diag. 
Line 9. 



Line 8. 



30 

52 

57 

48 

32 



Line 7. 





43 

52 

45 

Gate. 

28 + 52. 

76 

42 



Line 6. 



Part IV.) LAND-SURVEYING. 



159 





Finis. 






ToH. 






895 


Diag. 


}o from 


B, 

"ToB~ 


Line 16. 




720 







600 


40 




500 


48 




460 


Gate. 




400 


32 




350 


18 




300 


28 




200 


68 




100 


55 




000 


34 


Go from 


K, 


Line 15. 


To 


the 


Fence. 




580 


28 


ToK 


546 


30 




500 


32 




400 


46 




300 


45 




200 


40 




100 


34 




000 





Go from 


H, 


Line 14. 




ToG 






908 


Diag. 


Go from 


c, 


Line 1 3. 




ToC 







624 




54 


500 




65 


400 




63 


300 




52 


200 




30 


100 







000 




Go from 


H, 


Line 12. 




ToH 






750 







700 


18 




600 


38 




490 


60 +35 




350 


104 




220 


15 +80 




100 


25 




000 


30 


Go from 


o, 


Line 11. 



160 land-surveying. (Part IV. 



Answer. 

Having drawn the plan, you will find the perpendiculars of 
the different trapeziums to measure as follow : viz. 
D m = 426, and B n = 400, in No. 1 ; 
C m = 503, and F n — 44S, in No. 2 ; 
H n = 515, and E m = 498, in No. 3 ; and 
Cd = 428, and K m = 439. in No. 4. 



ABBA OF NO. 1. 

Double areas. 

821870 Trapezium A B C D. 
84786 Offsets on A B. 
64890 Ditto on B C. 

72968 Ditto on A D, 
1034514 Sum. 

93790 Insets on C D. 
2)940724 Difference. 

4.70362 Area in square links. 
4 



2.S1448 
40 



32.57920 Area 4a. 2r. 32^p. 



AREA OF NO. 2. 

Double areas. 

917715 Trapezium D C E F. 
93790 Offsets on C D. 
55510 Ditto on D F. 

1067015 Sum. 

60758 Insets on C E. 
43590 Ditto on E F. 

10434S Sum. 



962667 Difference. 

Area 4a. 3r. 10p. 



Part IV.) I.AND-SUKVEYING. l()l 

AREA OF NO. 3. 

Double areas. 

919804 Trapezium C E G H. 
60758 Offsets on C E. 
42480 Ditto on E G. 
81310 Ditto onG H. 

1104352 Sum. 

54096 Insets on C H. 

1050256 Difference. 

Area 5a. Ir. Op. 



AREA OF NO. 4. 

Double areas. 

775965 Trapezium B C H K. 

54096 Offsets on C H. 

41024 Ditto on H K. 

57200 Ditto on K B. 
928285 Sum. 

54890 Insets on B C. 
873395 Difference. 



Area 4a. Ir. 18|p. 



No. 
1. 


CONTENT. 


A. 

. 4 
. 4 
. 5 

. 4 

. 19 


R. P. 

2 32£ 

3 10 


2 




3 




1 


4 




1 18J 
21 


Sum 





Note 1. — In the last example, every field is measured separately ; but they 
are so connected by the chain-lines, that no difficulty can arise to the learner, 
in planning them. It may also be observed that no proof-lines were mea- 
sured ; but they should never be omitted in practice. If they be, the Sur- 
veyor cannot depend upon the accuracy of his work. 

M 



162 land-surveying. (Part IV. 

2. — If the foregoing Estate be laid down upon a sheet of drawing paper, 
by a scale of one chain, or of two chains to an inch, a finished Plan may 
then be made, and ornamented with Indian ink, in a similar manner to 
Plates IX. and XL Or the quick-wood hedges may be made by a pen and 
Indian ink ; or they may be represented by running narrow shades of 
colouring along the lines which form the boundaries of the fields ; and each 
field may then be washed over with a different colour, mixed up thinly with 
water, and laid on with a small brush, or camel's hair pencil. (See Part V. 
for the method of transferring a rough Plan to a clean sheet of paper, in 
order to make a finished Plan, with proper embellishments.) 

3. — In drawing the finished Plan, all the out-boundaries may be con- 
sidered as belonging to the fields which they respectively adjoin ; that 
fence from B to C. may be made as belonging to No. 1 ; that from C to D, 
as belonging to No. 2 ; that from C to E, as belonging to No. 3 ; and that 
from C to H, as belonging to No. 4. (See a remark on the 39th page, re- 
lating to fences.) 

4. — The title of the finished Plan of the foregoing Estate, may run thus : 
Plan of an Estate lying in the Parish of Bradford, in the West-Riding of 
the Countv of York, 



PROBLEM IV. 

MEREs AND WOODS'. 

The method of measuring Meres and "Woods by the Chain 
and Cross, has already been shewn in Part III. It is here pro- 
posed to survey them by the Chain only. 

In this case, you must not only measure on the outside of the 
mere, or wood, and take insets as before directed ; but also take 
such external angles, or tie-lines, as will enable you to lay down 
the figure. 

EXAMPLE. 

Let the following figure represent a mere, the area of which 
is required. 



Part IF.) LAND-SURVEYING. 163 

AS 



1 ,'••• 




Begin at -f- 1, and measure eastward as far as -f 2, taking 
insets as you proceed ; then produce the line to -j- 3. Return 
to -j- 2, and measure northward as far as -j- 4 ; thence run a 
line backward to -f- 3, which will tie the first and second lines. 
Return to -f- 4, continue the line to -f- 5, and produce it to 
+ 6. — Return to -f 5, and proceed westward to -J- 7> * ne di s ~ 

M 2 



16-4 



LAND-SURVEYING. 



(Part IV. 



tance between which and 4- 6. being measured, will tie the 
second and third lines. Return to + ?, and continue the line 
to 4- 8. From -|- 8 proceed to -f- 1, and you will have ob- 



tained the following dimensions. 



Note. — Here it may be observed, that after the first three lines are laid 
down, the fourth line will exactly reach from + 8 to + 1 ; if the operations 
have been performed with correctness. 






1625 


to 4- I. 


60 


1100 

iooo 




23 


800 




30 


600 




60 


96 







ooo 




From 


+ 8, 


go S. 





1150 


to 4- 8. 


100 


1100 
1000 







900 







700 


- 


40 


400 


4- 7. which is 550 





000 


from 4- 6. 


Return to 


-4- 5. and 


goVT. 




2000 


to 4- 6. 





1650 


+ 5. 


56 


1300 







1000 







550 






400 


4- 4. which is 490 


40 


300 


from + 3. 


103 


48 







000 




Return to 


+ 2. and 


cro N. 




1500 


to 4- 3. 





1200 


+ 2. 


50 


1100 

iooo 







850 







600 




100 


400 




80 


250 







000 




Begin at 


+ i, 


Range E. 



Part IV.) LAND-SURVEYING. 165 

Answer. 
Having constructed the figure, you will find the diagonal, 
drawn from -+- 1 to -f- 5 = 2085, the perpendicular from -f- 2 
upon the diagonal = 950, and that from + 8 = 890 links. 

Double areas. 

3836400 Trapezium made by stations 1, 2, 5, and 8. 
84500 ) 1 line ( 

87380 (2 J Insets taken on the 

53000 (3 ) different lines. 

118120 j 4 ( 

~343000 Whole Insets. 

3493400 Mere, Area 17a. 1r. 35p. 



PROBLEM V. 

TO MEASURE AND PLAN ROADS, RIVERS, 

CANALS, S?c, 

In measuring Roads, Rivers, or Canals, angles or tie-lines 
must be taken at the different turns, in order to lay down the 
chain-lines ; and offsets must be taken to the boundaries, as 
you proceed, to enable you to draw the plan. 

Note 1. — The length of a road is generally returned either in miles, fur- 
longs, and poles, or else in miles and yards. (See the Table, page 43.) 

2. — A machine called a " Perambulator" is sometimes used to ascertain 
the lengths of roads. It has a wheel of 8 feet 3 inches, or half a pole, in 
circumference, which being made to pass over the ground, puts in motion 
the clock-work within, and the distance measured is pointed out by an index 
on the outside. This instrument is much more expeditious for measuring 
the length of a road, than the chain ; but it is certainly less correct ; for by 
the wheel passing over stones, sinking into holes, &c the distance is made 
to appear more than it is in reality. 

EXAMPLES. 

1. Let the following figure represent a serpentine road, a 
plan of which is required. 

M -J 



166 



LAND-SURVEYING. 



(Part IV. 




3 ( 



Be°in at + 1. and measure to + 3, taking offsets on both 
sides, as you proceed. Return to + 2, and measure to + 4, 
from which run a line to + §•> """hich iwD tie the first and 
second lines. Return to -f- 4, and continue the line to + 6. 
From -r 6, proceed as before, until you arrive at -f 14 ; and 
you will have obtained the following dimensions, from which 
a plan may be drawn, 



Part IV.) LAND-SURVEYING.. 



167 





To + 14. 




58 


350 


60 


68 


200 


44 




150 


+ 13 is 184 from + U 


50 


100 


80 


Go from 


+ 12, 


Line 5. 




To + 12. 




30 


720 




,70 


6.50 






600 


+ 11. 


86 


550 


33 


70 


300 


50 


8 is 200 from -f 10 


200 




120 


135 


Cross-fence. 


Go from 


+ 9, 


Line 4. 




To + 9. 






700 






600 


Cross-iience. 




500 


+ 8. 


38 


480 


84 


40 


300 


60 


52 


180 


65 




150 


+ 7 is 160 from + 5. 


50 


100 




Go from 


+ 6, 


Line 3. 




To + 6. 




20 


512 




50 


450 




52 


380 


70 




350 


+ 5. 


20 


300 


80 




200 


+ 4 is 232 from + 3. 


18 


100 


93 


Go from 


+ 2, 


Line 2. 




To + 3. 






600 






480 


Cross-fence. 




400 


4-2 


38 


350 


95 


15 


300 




28 


200 


80 


55 


000 


70 


Begin 


at -|- 1, 


Line 1. 



M 4 



168 land-surveying. (Part IV. 

2. Let the foregoing figure represent a river, a plan of which 
is required. 

Begin at a, and measure to c ; taking offsets to the river's 
edge, as you proceed. From c measure to d ; and there take 
the tie or chord-line d b, which will enable you to lay down 
the first and second lines. Continue the second line to n ; and 
from m, measure to r, at which place take the tie-line r n ; and 
thus proceed until you come to the end of your survey at x. 

If the breadth of the river be every where nearly the same, 
its breadth taken in different places, by the next Problem, or 
by Problem 10, Part III. will suffice ; but if it be very irregu- 
lar, dimensions must be taken on both sides, as above. 

"When the area is required, it must be found from the plan, I 
by dividing the river into several parts ; and taking the neces- 
sary dimensions by the scale. 

Note. — Any Bog, Marsh, Mere, or Wood, whatever may be its number of 
sides, may be measured by this Problem. 



Part IV.) 1 AND-SURVEYING. 



169 



PROBLEM VI. 
TAKING DISTANCES B Y THE CHAIN AND SCALE. 



EXAMPLE. 

Required the distance of an object at A, from B. 

First, make a station at B ; then, 
in a direct line with B A, set up a 
pole, suppose at C ; measure the 
distance B C. Return to B, and 
measure in any direction, making an 
angle with B C, suppose to D ; 
then set up a pole in a direct line 
with D A, as at E. Measure the 
lines D E and E C, and also the 
diagonal C D ; these will enable 
you to construct the trapezium B 

CED. 

The lines B C and D E, pro- 
duced, will evidently meet at A. 

Measure the line B A with the 
same scale, by which you have con- 
structed the trapezium, and it will 
be the distance required. 

Note. — This method may be well applied 
to measuring the breadth of a river, or the 
distance of any inaccessible object ; and any 
person, acquainted with trigonometry, may 
easily find the correct distance, after mea- 
suring the lines before mentioned. 




170 



LAND-SURVEYING. 



(Part IF. 



PROBLEM VII. 

TO ERECT A PERPENDICULAR BY THE CHAIN, 
OR TO MEASURE LINES UPON WHICH THERE 
ARE IMPEDIMENTS. 

EXAMPLE. 



Suppose C D E F to represent 
the base of a building, through 
which it is necessary a line should 
pass to an object at B, seen from 
A. 

Measure from A to m ; and from 
m, measure back to a, 40 links. 
Let one end of the chain be kept 
fast at a, and the eightieth link at 
m; take hold of the fiftieth link, 
and stretch the chain so that the 
two parts a n. and m n, may be 
equally tight : then will m n be 
perpendicular toam, 

For m n will be 30, a m 40, 
and a n 50 links; or the sides of 
the right-angled triangle a m n 
will be in proportion to each other 
as 3, 4, and 5. (See Prob. 18. 
Part L) 

Measure from m, upon the line m 
n continued, until you are clear of 
the impediment, as at c ; then con- 
tinue the line 40 links farther, to b. 




*A 



Find by the above process 
the perpendicular c d j and proceed in that direction till you are 
beyond the building, as at h. Again erect the perpendicular 
h e, upon which measure till you have made h p, equal tome; 



Part IV.) LAND SURVEYING. 171 

and you will then be in a direct line with m A. Erect the per- 
pendicular p x, which (if you have conducted the work with 
correctness,) will be in a right line with B. Measure the dis- 
tance p B ; then A m, added to c h (= m p), and p B, will 
give the whole length of the line A B. 



PROBLEM VIII. 

HA VING THE PLAN OF A FIELD, AND ITS TRUE 
AREA, TO FIND THE SCALE BY WHICH IT HAS 
BEEN CONSTRUCTED. 

Rule. — By any scale whatever, measure such lines as will 
give you the area of the figure ; then say, as this area is to the 
square of the scale by which it was found, so is the true area, 
to the square of the scale required. 

EXAMPLE. 

Suppose the true area of a field, the plan of which is given, 
to be 9a. 1r. 32p. ; and that by a scale of 2 chains to an inch, 
I find the area to be 4a. Or. 32p. ; required the scale by which 
the plan was constructed. 

First, 9a. 1r. 32p. — 945000 square links; and 4a. Or. 32p. 
= 420000 square links ; then, as 420000 : 4 : : 945000 : 9. 
Hence, it appears, the plan was constructed by a scale of 3 
chains to an inch. 

N t e . — The principle of this process is, that the areas of similar figures 
are to each other as the square of their homologous sides. (Theo. 16, 
Part I.) 



172 LAND-SURVEYING. (Part IV. 



THE METHOD 



MEASURING HILLY GROUND. 



A line measured upon the acclivity or declivity of a hill, -will 
evidently exceed one measured upon the horizontal base ; con- 
sequently, if a plan be laid down by the hypothenusal lines, 
every part will be thrown out of its true situation ; so that the 
boundaries of a mountainous lordship would appear distorted 
and unnatural ; and the estate would scarcely be recognised by 
its own inhabitants. 

Surveyors, therefore, agree in their opinions concerning the 
necessity of reducing hypothenusal to horizontal lines, for the 
purpose of planning ; but they differ with regard to the modes 
of finding the area ; some contending that it should be com- 
puted according to the hypothenusal, and others according to 
the horizontal lines. 

The advocates for the horizontal measure assert, that no more 
corn, trees, &c. can grow upon the surface of a hill, than upon a 
space equal in area to its base, admitting both to be of the same 
quality ; and that hilly ground, in general, is less productive 
than plains, and its cultivation attended with more expense. 
The advocates on the other hand state, that the surveyor has 
nothing to do with the quality of the land ; and that it is his 
duty to return the measurement of the surface, and leave the 
value to those whom it more nearly concerns. 

The horizontal measure, however, is now generally adopted, 
except for paring, reaping, &c. in which cases the hypothenusal 
measure is very justly preferred. (See Deut, xxiv. 14, 15 ; and 
Prov, xxii, 16.) 



Part IV.) LAND-SUllVEYING. 173 



Methods used by Practical Surveyors to reduce hypothenusal to 
horizontal Lines. 

METHOD I. 

When the hill is of a regular slope, take its altitude with a 
Theodolite, or with a Quadrant ; then, by a trigonometrical 
canon, in which the hypothenuse may be counted 100 links, 
determine the number of links in the base. These deducted 
from 100, will shew the number of links by which each chain 
must be shortened, for the purpose of planning. 

Note. — For the principles of Trigonometry, the reader is referred to the 
works of Simpson, Emerson, Vince, Horsley, Keith, Bonnycastle, and the 
Rev. W. Wright, on that subject ; and for the history, construction, and 
use of Logarithms, to Dr. Hutton's Mathematical Tables. 

EXAMPLE. 

Suppose the altitude of a hill to be 16° 15', and the length of 
a line measured upon its surface, to be 2550 links ; required 
the length of the line, that must be used in planning. 




In the right-angled triangle ABO, are given the hypothenuse 
A C =. 2550, and the angle B A C = 16° 15', to determine the 
base A B. Or A D = 100, and the angle EAD = 16° 15' 
to find A E. 

As Radius 1 0.00000 

Is to the hypoth. A D — 100 links 2.00000 

So is the co-sine of the angle E AD = 16° 15' ... 9.98229 
To A E = 96 links 1798229 



in 



I. AND SURVEYING. 



(Part IV. 



Hence it appears, that 4 links must be subtracted from each 
chain; consequently, (25 X 4 -f- 2 =) 102 links must be taken 
from A C ; hence AB = 2448 links, the line required. 

Proof. — As 1 : 2550 :: .96005 (the nat. co-sine of 16° 15') 
: 2448.1275 links — A B. 



A Table for reducing hypothenusal to horizontal Lines. 



Different 

Altitudes 

of 

Hills 


Links to be 

subtracted 

from each Chain 


measured upon 




the Surface. 


Deg. Min. 


Links. 


5 44 


h 


8 6 


1 


11 28 


2 


14 4 


3 


16 16 


4 


18 12 


5 


19 57 


6 


21 34 


7 


23 4 


8 


24 30 


9 



Deg. Min. j Links. 



25 


51 


10 


27 


8 


11 


28 


21 


12 


29 


32 


13 


30 


42 


14 


31 


47 


15 


32 


52 


16 


33 


54 


17 


34 


55 


18 


35~ 


54 


19 


36 


52 


20 


37 


49 


21 


38 


44 


22 


39 


39 


23 


40 


32 


24 



Note. — To construct the above Table, suppose the base A B, in the pre- 
ceding triangle, to be = 99.5, and the hypothenuse A C = 100 ; then, by 
Trig, as 100 : 1 :: 99.5 : .995, the nat. co-sine of the angle B A C= 5° 44'. 
— In the same manner, the rest of the angles are obtained, by different opera- 



third, &c, 



Part IV.) LAND-SURVEYING, 



175 



A Quadrant for taking the altitude of Hills , Steeples ■> fyc. 




By those who do not wish to incur the expense of a Theo- 
dolite, a Quadrant may be made of about twelve inches radius, 
by which the altitude of a hill, steeple, &c. may be taken to a 
tolerable degree of accuracy. 

The arc A B must be correctly divided into 90 equal parts 
or degrees ; and numbered from right to left. Upon the radius 
A C, must be fixed two brass sights, a and b, through each of 
which must be made a very fine hole ; and from the centre C 
must be suspended a plummet, by a thread of fine silk. 



176 land-surveying. (Part IV. 

Note. — In taking the altitude of an object, the quadrant is commonly held 
in the hand ; but it is much better to fix it to a staff, which may be done by 
means of a nail, passing through the quadrant and staff, upon the end of 
which must be screwed a small nut. 



To take the Altitude of a Hill with the Quadrant. 

Upon the top of the hill fix an object, exactly as high as 
yonr eye 'will be from the ground, in taking the observation. 
At the bottom of the hill, fix the quadrant-staff perpendicularly 
to the horizon ; which may be easily done by means of the 
plummet. Then with one eye at A, the other being closed, 
look through the sights, turning the quadrant until you per- 
ceive the object at D; so will the arc B G, cut off by the 
plumb-line C G, be the measure of the angle D C E, or the 
altitude of the hill, in degrees, &c. 

Note. — When you take the altitude of a hill by a Theodolite, the obser- 
vation must be referred to an object fixed upon the top of the hill, exactly 
as high as the telescope. 



To take the Altitude of a Steeple, §c. with the Quadrant. 

Screw the quadrant fast to its staff, so that the plummet may 
hang exactly at 45°, when the staff is perpendicular to the hori- 
zon. Then, move the staff backward or forward (always keep- 
ing it perpendicular) until you can see the top of the object 
through both the sights. Measure the distance between the 
bottom of the staff and that of the object, which being added to 
the height of your eye, will give the altitude required, 



METHOD II. 

As the foregoing method of reducing hypothenusal to hori- 
zontal lines, can only be applied, with accuracy, when hills are of 
a regular slope ; surveyors, in general, elevate the chain, as they 
ascend or descend a hill, in order to preserve the horizontal line. 



Part IV ) 



LAND-SURVEYING. 



177 



EX \ MPLE8. 





i 


L— ]n 




a>- 




V. 




^ 


r c 






w- \ 








g 



D 



c 



Suppose the lines A I> and B C, to represent the acclivity and 
declivity of an irregular liill ; it is required to raeasue them, 
and to preserve the horizontal line A ('. 

i A. stretch the chain toward B, and suppose it to reach 
to a ; th stent, upon the hase, will evidently reach from 
A to g ; and a perpendicular erected from g will intersect the 
line A B in d ; hence the distance A d, upon the hypothenuse, 
will make one chain upon the hase At A, stick your offset- 
staff into the ground, perpendicularly to the horizon, and let 
your assistant hold the chain, suppose at the twenty-fifth link, 
close to the surface of the hill, as at b ; at the same time you 
must elevate tie- end of the chain to c, forming the horizontal 
line c b ; then move forward to b, at which place fix your staff 
Let your assistant hold the fiftieth link at p, 
whi! the twenty-fifth to n, forming the horizontal 
line n p. Again, fixing your staff at p, elevate the fiftieth link 
to m, while your assistant holds the Beventy-fifth at e. Lastly, 
put down the staff at e. and elevate the seventy-fifth link to r, 
while the hundredth is held by your assistant at d. There he 
• put down an arrow ; and thus you must proceed until you 
arrive at I>, where you will have ohtained the horizontal line 
A D. 

In descending from B to C, let your assistant hold one end of 
the chain at B, whilp you elevate, suppose, the fiftieth link to n. 

N 



178 LAND-SUBVEYING. P< rt IV. 

forming the horizontal line B n ; then fix the staff at a. perpen- 
dicularly to the horizon, and touching the chain at n. Xext. 
at hold the fiftieth link at a. while you elevate 
the hundredth to m, and put down the staff at r, as before. In 
this manner, having arrived at C. you will r ained the 

ntal line D C, which I ~e the 

ratal line A C. as requL 



1. — If you wish to obtain the hypothenusal, as well as the horizontal 
line, divide your field-book into four columns, in one of which you mu- 
the number of links between a and d, «Jcc. which being added to the horizon- 
tal, will give the hypothenusal line. 

2. — When ^eent of a hill is great, you will not be able to 

more than 10 or 15 links of the chain at one time ; for, in such cases? 
rtempt to r I : U find that the perpendiculars 

A c, b n, &c will exceed your own height, before you can form the fa 
talline-: . . ire.) 



-METHOD in. 

Hypothenusal lines may likewise he expeditiously and cor- 
rectly reduced to horizontal by an 
instrument invented by Mr. Robert King, of Scarborough,. 
Land-Surveyor, and caD i nt." 



THEDESCRHTIONAND USE OF KING's SURVEYING 
QUADRAXT. 

by TT'. Jonas, M 

I: 

DESCRTPT 

s: Tkf. quadrant is fitted to a wooden square, which - 
upon a -staff, and may be fixed at any height by rat 

a screw, which draws in the diag : staff; thus em- 

bracing the four sides . the limb of the square per- 

pendicular to with iron, 

I, on the 



Part IV.) land-survuyixg. 179 

station -line, the square answers the purpose of a cross-staff, and 
may, if desired, have sights fitted to it. The quadrant is three 
inches radius, of brass, is furnished with a spirit-level, and is 
fastened to a limb of the square, by means of a screw. 

When the several lines on the limb of the quadrant have their 
first division coincident with their respective index-divisions, 
the axis of the level is parallel to the staff. 

The first line next the edge of the quadrant, is numbered 
from right to left, and is divided into 100 parts, showing the 
number of links in the horizontal line, which are completed in 
100 links on the hypothenusal line, and in proportion for any 
smaller number. 

The second, or middlemost line, shows the number of links 
the chain is to be drawn forward, to render the hypothenusal 
measure the same as the horizontal. 

The third or uppermost line, gives the perpendicular height, 
when the horizontal line is equal to 100." 



USE. 

" Lay the staff along the chain-line on the ground, so that 
the plane of the quadrant may be upright ; then move the 
quadrant, till the bubble stands in the middle, and on the 
several lines you will have, — 1. The horizontal length gone 
forward in that chain. 2. The links to be drawn forward to 
complete the horizontal chain. 3. The perpendicular height or 
descent made in going forward one horizontal chain. 

The first two lines are of the utmost importance in surveying 
land, which cannot possibly be planned with any degree of 
accuracy without having the horizontal line ; and this is not to 
be obtained by any instrument in use, without much loss of 
time to the surveyor. Whilst with this, he has only to lay his 
staff along the ground, and set the quadrant till the bubble is 
in the middle of the space, which is very soon performed. And 
he saves by it more time in plotting his survey, that he can 
lose in the field ; for as he completes the horizontal chain as he 

N 2 



180 land-surveying. (Part IV. 

goes forward, the offsets are always in their right places, and 
the field-book being kept by horizontal measure, his lines are 
sure to close. 

If the superficial content, by the hypothenusal measure, 
be required for any particular purpose, he has that likewise, 
by entering in the margin of his field-book the links drawn 
forward in each chain, having thus the hypothenusal and hori- 
zontal length of every line. 

The third line, which is the perpendicular height, may be 
used with success in finding the height of timber. Thus, 
measure with a tape of 100 feet, the surface of the ground from 
the root of the tree ; and find, by the second line, how much the 
tape is to be drawn forward to complete the distance of 100 
horizontal feet ; and the line of perpendiculars shows how 
many feet the foot of the tree is above or below the place where 
the 100 feet distance is completed. — Then, inverting the 
quadrant by means of sights fixed on the staff, place the staff 
in such a position, as to point to that part of the tree whose 
height you want ; and sliding the quadrant till the bubble stands 
level, you will have on the line of perpendiculars on the qua- 
drant, the height of that part of the tree above the level of the 
place where you are ; to which add or subtract the perpen- 
dicular height of the place from the foot of the tree, and you 
obtain the height required." 

Note i. — If the real utility of Mr. King's Surveying Quadrant was better 
known among Land-Surveyors, it would be in more estimation ; and would 
save them a great deal of trouble in measuring hilly ground. It may be had 
of Mr. W. Jones, price If. 18s. 

2. — For the sake of those who may think Mr. King's Quadrant too expen- 
sive, I have invented one of a cheaper kind, which answers the same purpose 
in surveying, as Mr. King's, and may be used with equal facility. Any com- 
mon mechanic will be able to make the wood-work ; and after the lines are 
drawn upon the plate, an engraver will cut them for about five shillings. 
The whole expense of one which the Author had made for his own use, five 
inches radius, together with the offset-staff belonging to it, amounted to about 
twelve shillings. 



Hiiro II. 



"/> 




J3 I /// E G- Q--fe 




Part IV.) LAND-SURVEYING. 



181 



The following Table, by which the Quadrant may be constructed, 
shows the Number of Links to be drawn fonoard upon the Sur- 
faces of Hills of different Altitudes, to complete the horizontal 
Chains. 





Deg.Min 
5 43 


Lks. 
i 


Deg 
41 


Min. 

~44~ 


Lks. 


Deg 


.Mm 


Lks. 






34 


53 


~~ 28" 


~68~ 






8 4 


1 


42 


12 


35 


58 


43 


69 






11 22 


2 


42 


40 


36 


53 


58 


70 






13 52 


3 


43 


7 


37 


54 


13 


71 






15 51 


4 


43 


34 


38 


54 


27 


72 






17 45 


5 


43 


59 


39 


54 


41 


73 






19 22 


6 


44 


25 


i 40 


54 


55 


74 






20 50 


7 


44 


50 


1 41 


55 


9 


75 






22 12 


8 


45 


14 


42 


55 


23 


76 






23 27 


9 


45 


38 


1 43 


55 


36 


77 






24 37 


10 


46 


1 


44 


55 


49 


78 






25 43 


11 


46 


24 ' 45 


56 


2 


79 






26 46 


12 


46 


46 


46 


56 


15 


80 






27 45 


13 


47 


8 


47 


56 


28 


81 






28 42 


14 


47 


30 


48 


56 


40 


82 


i 




29 35 


15 


47 


51 


49 


56 


53 


83 






30 27 


16 


48 


11 


50 


57 


5 


84 






31 16 


37 


48 


32 


51 


57 


17 


85 






32 4 


18 


48 


52 


52 


57 


29 


86 






32 49 


19 


49 


11 


53 


57 


40 


87 






33 33 


20 


49 


30 


54 


57 


52 


88 






34 16 


21 


49 


49 


55 


58 


3 


89 






34 57 


22 


50 


8 


56 


58 


15 


90 






35 37 


23 


50 


26 


57 


58 


26 


91 






36 15 


24 


50 


44 


58 


58 


37 


92 






36 52 


25 


51 


2 


59 


58 


48 


93 






37 28 


26 


51 


19 


60 


58 


58 


94 






38 3 


27 


51 


36 


61 


59 


9 


95 






38 38 


28 


51 


53 


62 


59 


19 


96 






39 11 


29 


52 


9 


63 


59 


30 


97 






39 43 


30 


52 


26 


64 


59 


40 


98 






40 14 


31 


52 


42 


65 


59 


50 


99 






40 45 


32 


52 


58 


66 


60 





100 




'J 


41 15 


33 J 


53 


13 


67 











N 3 



182 



LAND-SURVEYING, (Part IV. 



The Construction of the preceding Table. 

C 




In the right-angled triangle A B C, suppose the base A B to 
be 100, and the hvpothenuse A C 100.5 ; then by Trig. 
as 100. 5 : 1 :r 100 : .99502, the nat. co-sine of the angle 
BAG — 5° 43'. — In the same maimer, the rest of the angles 
are obtained, by different operations, accounting the hypothenuse 
101 in finding the second angle, 102 in finding the third, &c. — 

Now, from the preceding Table, it evidently appears, that 
if an instrument be constructed to take the altitude of a hill at 
every chain, if necessary, and a line traced upon the instrument, 
be so divided as to exhibit the number of links which the chain 
must be drawn forward, upon the surface of the hill, to com- 
plete the horizontal chain, according to the Table ; it may 
be used with great advantage in surveying h ill v ground. 



The method of constructing the Quadrant, Sfc. 

Procure a piece of soft sheet-brass, and upon it draw the 
lines A B and A C perpendicular to each other ■ and with a 
radius of five inches describe the quadrant B C. 

Next, draw the lines D E and D F perpendicular to each 
other ; and with four inches in your compasses for the first 
sweep, describe the double arc E F, which divide correctly 
into 90 equal parts or degrees. At a proper distance, likewise, 
from the arc E F describe the double arc G H, and the double 
arc m n. Of these, the latter must be cut through the brass by 
a file. 

You must also procure a small glass tube, nearly filled with 
spirit, (generally called 4 a spirit-level,') and a piece of sheet- 



Part IV.) LAND-SURVEYING. 183 

brass K L, in length equal to A B, and in breadth rather 
exceeding the diameter of the tube ; which call " the 
Index." 

Then procure another piece of sheet-brass in the form of a 
semi-cylinder N P, large enough to admit the tube ; and in it 
make the aperture b c d, in order to see the bubble. 

Its edges solder to the index K L, so that the centre c may be 
exactly in the middle point between r and a ; r a rather exceed- 
ing D E ; and a u being exactly equal to D m. The end N 
must also be closed up, by soldering a piece of brass upon it ; 
and the end P left open, in order to admit the tube. 

Next make a wooden quadrant, exactly the size of A B C, and 
in it a grooye corresponding with the aperture m n, and large 
enough to admit a small screw-nail, with a square head and 
neck, so as to run, but not to turn round in the grooye m n. 

Then fix the plate A B C to the wooden quadrant, by the 
countersunk screws, 1, 2, 3, 4, 5 ; taking care first to insert the 
screw-nail aboye-mentioned, into the aperture m n, at a small 
hole made for that purpose at n. 

Next, let the index K L be fixed upon the face of the qua- 
drant, by a screw-nail passing through it at a, which must enter 
the quadrant exactly at the centre D. The nail in the aperture 
m n must likewise pass through the hole at u, and upon the 
end of this nail must be screwed a small nut, by which the end 
K of the index may be made fast at any altitude. 

Now, to diyide the arc G H, moye the end K of the index 
toward C, until the line or edge r e, which must be exactly in 
the centre of the index, cuts the arc E F at 8° 4', as per Table ; 
and upon the arc G H, mark the first division. In the same 
manner, moye the index until it cuts off 11° 22', and there mark 
the second ; continuing these operations, until you haye made 
as many divisions as are necessary. — The divisions marked upon 
the arcs E F and G H, must then be properly cut and figured 
by an engraver. 

Next procure a wooden cross, R T S W, the three limbs of 
which must each be in length equal to A B or A C ; and must 
form with each other three right angles, R S T, T S W, and 
WSR. 

N 4 



184 land-surveying. (Part IV. 

This cross must be made to slide upon an offset-staff by means 
of a square or rectangular aperture through the limb R S ; and 
if a screw be fixed in the side of the limb at n, the cross may 
be fastened to the staff at any convenient height, by turning 
the screw against the side of the staff. As it will be somewhat 
difficult, however, on account of the limb R S being hollow, to 
make a joint at S sufficiently strong to keep the limbs at right 
angles with each other, they may be supported by means of the 
brackets, a b, c d, and e f. The quadrant ABC must then 
be fixed upon the square R S T, by means of two screws pass- 
ing through the bracket a b, and one through the bracket m, so 
that the outside of the limb S R may coincide with A B, and 
the outside of the limb S T with A C. 

To fix the tube or spirit-level correctly in the semi-cylinder 
N P screw the index fast at no altitude, and place the edge 
A B of the quadrant upon a level table, which you may do by 
laying the tube upon it, and varying the position of the table 
until the bubble stands in the centre of the tube ; then put the 
tube into the semi-cylinder N P, and fix it in such a manner 
that the bubble may be seen at c ; after which, close up the 
end P with brass or putty. 

Note. — If the quadrant be made the same size as that in Plate II., instead 
of five inches radius, as before directed, it will save much trouble in di- 
viding ; as the engraver may then follow the divisions given in the Plate ; 
and the construction of this useful instrument will thus become very simple. 



The Method of proving the Quadrant, 

C 




B 



Part IV.) LAND-SURVEYING. 185 

Let AC b strong plank, placed with one end against 

the perpendicular wall B C, and the other npon the horizontal 
plane A B. Lay an offset-staff, suppose of 12 links, upon A C, 

with one end at A ami the other at m ; then elevate the lower 

i that the stall' a n may he parallel to A \\. Measure the 

i d, which suppose to be 10.5 inches \ then say, as 

12 link* is to 10.5 i is l"<) links to 87.5 inches, or 11 

links. 

A B of the quadrant upon the plank A ( . 
the end Iv of the index, until the bubble stands at 
I if the index cut off 11 links, or nearly BO, upon the are 
OH, the quadrant us 



The Method ofuting the Quadrant. 

the stafi 1 ', with the quadrant fixed to it, along the chain- 
that the edge A B of the quadrant may come in contact 
with the pound; then elevate the end K of the index, until 
the bubble stands at C ; and you will have the altitude of the 
hill upon the are 1] J\ and the number of links to be drawn 
forward to complete the horizontal chain, upon the arc G H. 
If you lix the bottom of the staff into the ground, upon the 
chain-line, the limbs S T and S W will serve as a cross, by 
which perpendiculars may be erected. 

I . — In using the quadrant, care should be taken to place it upon the 
even part of the surface of the hill. 

. measuring and reducing a line upon a hill, if it happen that the 

end of the chain reach' .at the end of the line, you 

n deduct from the chain instead of drawing it forward. i\, r ex- 

: if yon fmd that tlu- chain oughl to be drawn forward 6 links, you 

instead <»f 100 links. Or, if tin- fiftieth link reach to the 

station, istead of 50 links, \c. 

[nine, by < I chain, and aKo 1 iv the Quadrant. 

thr number of link iwn forward upon the surface of i hill, in order 

ri/.ontal chain, you will seldom find them precisely the 



183 land-surveying. (Part IV. 

same ; because it is almost impossible to prevent the chain from forming a 
curve line, or to keep the staff perpendicular to the horizon. In every case 
however, the conclusions of an instrument, constructed upon mathematical 
principles, are to be preferred. 



Methods for finding the kypotkenusal Measure of Hilly Ground. 

This is by far the most difficult part of surrevinp; ; and 
though we may approach ' toward, we can seldom obtain the 
true area of hills ; because their surfaces are generally so irre- 
gular, that it is almost impossible to divide them into proper 
figures. — 

If the land to be surveyed, lie in the form of a square, rect- 
angle, trapezoid, trapezium, or triangle, against the side of a 
hill of a regular slope, take the dimensions and find the area in 
the same manner as if the figure lay upon a plane. But should 
it be required to find the area of a field (suppose in the form of 
a trapezium) in which there is a hill so situated as to affect the 
diagonal only ; if the sides and diagonal be measured, and the 
figure laid down according to those dimensions, the perpendi- 
culars will obviously measure less than they would have done, 
had the diagonal been reduced to a-horizontal line ; consequently, 
we cannot obtain the hypothenusal measure of such a field, by 
the common method of measuring trapeziums, or triangles. 

In such cases, it is perhaps best, first, to measure the hill only. 
For this purpose, surround its base by station-staves, dividing 
it into an irregular polygon, each side of which must be mea- 
sured. Then fix upon a convenient place, near the top of the 
hill, for a station ; and between it and each station at the bot- 
tom, measure a line. Thus will the whole surface be divided 
into triangles, the areas of which, must be found by laying down 
each triangle separately. Or, from the three sides, you may 
find the area of each triangle, as already directed. 

Next, measure the remainder of the field, by dividing it into 
proper figures. Collect all the areas together, and their sum 
will be the area required. 

"When the land to be surveyed, ascends a hill on one side, 
occupies a plane upon the top, and descends on the other side ; 



Part IF.) LAND-SURVEYING. 187 

you must divide it into such figures as will enable you to ap- 
proach as nearly as possible to the true area. — 

The foregoing directions may, perhaps, be found useful to 
a learner ; but, in practice, much will always depend upon the 
Surveyor ; he ought, therefore, to be very careful, whatever be 
the shape or size of the hill, to divide it into such squares, rect- 
angles, trapezoids, trapeziums, or triangles, as are most likely 
to give him the hypothenusal measure. 

Note 1 . — In surveying a triangular field, of which one side passes over a 
hill, the other two being upon the horizontal plane of the base ; it will be 
necessary to divide it into two triangles, by measuring a line from some part 
of the fence passing over the hill, to the opposite angle. Thus will two sides 
of each triangle be affected by the hill, the areas of which, found separately, 
will give the hypothenusal measure of the field. 

2. — After making some experiments, and considering the subject very 
maturely, the Author is of opinion that the most correct method of finding 
the surfaces of hills, in general, is to take the dimensions in such a manner 
that the areas of the different figures into which the hills are divided, may 
be found from the lines measured in the field, without having recourse either 
to the scale or plan. Hence, if the figures be rectangles, their lengths and 
breadths must be measured in the field ; and if they be triangles, trapeziums, 
or trapezoids, their bases and perpendiculars must be measured in the field. 

Several very experienced Laud-Surveyors with whom the Author is ac- 
quainted, perfectly agree with him on this subject. 



EXAMPLES. 

1. The length (or hypothenusal line) of a rectangular field, 
lying upon the side of a hill of regular ascent, is found to be 
900 links, its breadth, 800 links, and the altitude of the hill 
28° 21'; required the hypothenusal measure, and the length 
of the line that must be used in planning : 

900 
800 

7720000 
4 

.80000 
40 

32.00000 Area 7a. Or. 32p. 



188 land-surveying. (Part IV. 

Now, by the Table, page 174, we find that 12 links must 
be deducted from each chain ; hence 9 X 12 = 108, which 
being taken from 900, leaves 792 links, the length of the line 
required. 

Note.— If we multiply 792 by 800, we find the product 633600 square 
links, equal to 6a. 1r. 14p. the horizontal measure, which is less than the 
hypothenusal by 3r. 18p. 

2. Let A B C D represent a field in the form of a trapezium, 
lying upon the side of a hill of an irregular ascent, the sides 
A B and B C being upon the horizontal plane of the base ; re- 
quired the horizontal and hypothenusal measures, from the 
following notes. 




I 



Part IV.) LAND-SURVEYING. 



189 





no 


BD 

1154 




6 




12 


1100 




11 


1000 




12 


900 




10 i 


800 




11 


700 




10 


600 




8 


500 




9 


400 




7 


300 




8 


200 




6 


100 


From 


B, 


goN. 






A C 






1300 






R. off A. 




78 


DA 

990 




6 




7 


800 




9 


700 




8 


600 




7 


500 




9 


400 




10 


300 




. 11 


200 




11 


100 
R. offD. 




96 


CD 

1044 




5 




10 


1000 




11 


900 




12 


800 




11 


700 




9 


600 




10 


500 




8 


400 




7 


300 




6 


200 




7 


100 
R. offC. 






BC 






800 






R. off B. 






AB 






700 


Begin 


at 


A. 

- 



Diag. 

Diag. reduced for 
a proof-line. 



Range S. TV. 



190 land-surveying. (Part IV. 



The Operation of finding the horizontal Measure. 

First, 700 -f 1154 -f 990 = 2844, the sum of the three 
sides, which being divided by 2, gives 1422. — From this num- 
ber, deduct severally each side, and we obtain 722, 268, and 
432, for the three remainders. Then, by multiplying the half 
sum and the three remainders continually together, and ex- 
tracting the square root of the product, we obtain 344768 
square links, the horizontal measure of the triangle A B D. 

In a similar manner, we find the horizontal measure of the 
triangle B C D = 405559 square links ; which, added to 
344768, gives 750327 square links, equal to 7a. 2r. the hori- 
zontal measure of the trapezium ABC D. — 



The Operation of finding the hypothenusal Measure. 

First, 1154 -f- 110 =: 1264, the hypothenusal line BD; 
and 990 + 78 — 1068, the hypothenusal line D A. Then, 
700 + 1264 -f 1068 — 3032, the sum of the three sides, 
which being divided by 2, gives 1516. From this number, 
deduct severally each side, and we obtain 816, 252, and 448, 
for the three remainders. Then, proceeding as before, we ob- 
tain 373709 square links, the hypothenusal measure of the 
triangle A B D. — 

In a similar manner we find the hypothenusal measure of 
the triangle BCD = 437917 square links, making jointly 
821626 square links, equal to 8a. Or. 34p. the hypothenusal 
measure of the trapezium ABCD, which exceeds the hori- 
zontal measure by 2r. 34p. 

Note 1. — If you lay down the trapezium by the horizontal and hypothe- 
nusal lines respectively,and measure the perpendiculars by the scale, you will 
find the areas the same as those resulting from the foregoing operations. 



Part IV.) LAND-SURVEYING. 191 

2.— From these examples, it appears that the difference between the hori- 
zontal and hypothenusal measures of hilly fields, is often very considerable, 
and is deserving of particular notice. For instance ; suppose the field, in the 
last example, to have been sown with wheat, and the owner to have sold the 
crop at the rate of 12/. per acre ; the reapers have a claim upon the buyer 
for the hypothenusal measure ; but if he makes his payment to the seller, by 
the same admeasurement, he will receive 8/. lis. more than his clue. 

Practical Surveyors, however, in general, (as before observed,) return the 
horizontal measure, in surveying estates ; whence few farmers, comparatively 
speaking, are charged for more ; and ought not, therefore, when they sell a 
crop of corn, &c. to expect pay for the hypothenusal measure. 



REMARK. 

Since the publication of the first edition of this Work, the 
Author has consulted several eminent Land- Surveyors, and also 
Commissioners for Inclosures, in very extensive practice, in the 
West-Riding of Yorkshire, and in Cumberland, and Westmore- 
land, places noted for their hills ; and they, without one ex- 
ception, inform him that the horizontal measure of hilly ground 
is always returned, both by them, and by every practical Sur- 
veyor with whom they are acquainted. 

Some late writers on Surveying contend very strenuously 
for the hypothenusal measure of hills ; but the Author and his 
friends have no hesitation in saying, that those writers are 
very deficient in practical knowledge. 

If we consider the earth as a perfect sphere whose diameter 
is 7957 miles, it is not necessary to take its curveture into con- 
sideration in surveying single Fields, Farms, or Lordships ; for 
it is evident that the quantity of land even in the County of 
York, would form such a small spherical segment, that its con- 
vex surface would exceed the area of its base extremely little. 

But we know that the hills upon the earth's surface are pro- 
tuberances, and the valleys are cavities, both of which tend very 
materially to destroy the globosity of the earth ; consequently 
it is evident that if the surfaces of all the mountains, hills, val- 
leys, plains, oceans, seas, rivers, lakes, Sec. &c. were measured 



192 land-surveying. (Part IV. 

separately, and then added together, the aggregate sum would 
greatly exceed the convex surface of the earth, measured as a 
perfect sphere ; hence the absurdity of the arguments of those 
writers who contend that all hills, however irregular, should 
be considered as bearing some similitude to a spherical segment^ 
or to a hemisphere of the earth. 

Now, as all hills are more or less irregular, the Author must 
confess that he is completely at a loss how to consider any hill 
as resembling the segment of a sphere ; much less Snowdon 
and Plinlimmon, in Wales ; the Peak, in Derbyshire ; Whernside 
and Ingleborough, in Yorkshire ; Helvellyn and Skiddaw, in 
Cumberland ; the Cheviot Hills, in Northumberland ; and the 
Grampian Hills, and Ben Nevis, in Scotland ; to say nothing 
of the Pyrenees, the Alps, the Apennines, the Carpathian, the 
Koelen, and the Uralian Mountains, in Europe ; and the still 
higher mountains of Asia, Africa, and America. 

But let us consider the subject on a less extensive scale ; and 
we shall still find that the advocates for the horizontal measure 
have the advantage, both with regard to practicability, expe- 
dition, accuracy, and justice. 

It may be seen by inspecting the figure on page 177, that it 
requires no more posts, fixed at a certain horizontal distance 
from each other, to extend over the surface of a hill, than would 
be required for the horizontal plane of its base, if the hill were 
actually removed. It is also well known that no more trees, 
corn, &c. will grow upon the surface of a hill, than upon a 
plane equal in area to its base ; because the natural direction of 
all vegetation is perpendicular to the horizon ; hence the in- 
justice done to the occupier, by returning the hypothenusal 
measure of hills. 

Again, if the area of a field containing hills and valleys, 
either natural or artificial, be found from lines measured on the 
surface, and the field be sold by this measurement, and it be 
afterwards levelled by filling up the valleys with the hills ; it is 
evident that the buyer will not have the quantity of land for 
which he paid, if the field be re-measured ; hence the injustice 
of selling ground by the hypothenusal measure. 

Lastly, it is evident that no more houses can be built upon 



Part IF.) LAND-SURVEYING. 193 

a hill, than what could be built upon its base, if the hill itself 
■were removed ; because the walls of all houses are perpendicular 
to the horizon, and their eaves parallel to it ; hence the buyer 
of building ground situated on a hill, forming an inclined plane, 
will be completely defrauded, if the ground be sold by the 
hypothenusal measure. 

The same observations are equally just in all cases, relating 
to the measurement of hills, except for labour performed by the 
acre, which should always be calculated from lines measured 
upon its surface ; because the spade, plough, si the, or sickle, 
must inevitably pass over the whole hypothenusal area. 

It may fairly be presumed that those writers who contend for 
the hypothenusal measure of hills universally, have never taken 
an actual survey of a mountainous district, where almost every 
line is affected by a hill, or they would have discovered the im- 
practicability of the method which they recommend. 

It is allowed by every one that the horizontal lines must be 
used, in order to produce a correct plan of a mountainous estate ; 
but when a plan by the horizontal lines, and the area by the 
hypothenusal lines are wanted, it is evident the Surveyor must 
not only have two sets of lines, but also two different plans laid 
down from those lines. 

One of those plans being laid down from the horizontal lines 
will exhibit the buildings, fields, rivers, &c. &c. in their natural 
situations ; and the other being laid down by the hypothenusal 
lines, will shew the surfaces of the hills extended on a plane : 
hence their hypothenusal areas may be found. 

Either this method must be followed, or the Surveyor must 
first take the horizontal lines for planning; and afterwards 
measure such lines on the surface of the ground, as will give 
him the hypothenusal area of the hills. 

Every professional Surveyor will readily perceive, that both 
these methods must be very liable to errors, without any pos- 
sibility of detecting them ; for neither in planning from hypothe- 
nusal lines, nor in finding the area from dimensions taken in the 
field, can we have the least proof of the accuracy of the work. 

And, if to these objections, we add the difficulties which will 
present themselves in taking the angle of elevation or depression 

o 



194 land-surveying. Pari IV. 

of erery hill with a theodolite ; the impossibility of doing this 
correctly, when a hill varies frequently in its inclination 
time that must necessarily be consumed in measuring rwo sets 
of lines : drawing two plans. together with the inac- 

curacies which must arise from such a multiplicity of operations, 
devoid of proofs ; it will manifestly appear that surveying, on 
these principles, is a theoretical dream, a labyrinth of perplexi- 
> aid a system of absurd: - 









LAND-SURVEYING. 



$art m dfiffi> 

THE METHOD OF SURVEYING AND PLANNING 
LARGE ESTATES, OR LORDSHIPS. 

V arious methods are adopted by different Surveyors, in taking 
the dimensions of large estates, or lordships ; I shall, however, 
describe only four, which I conceive to be more accurate and 
practical than any other with which I am acquainted. 

METHOD I. 

Having made yourself acquainted with the form of the estate, 
either by actual examination, or by the assistance of a previous 
plan, select two suitable places, at the greatest convenient 
distance from each other, as grand stations ; and measure a prin- 
cipal base, or what is generally called a " main-line," from one 
to the other, noting every hedge, brook, or other remarkable 
object, as you cross or pass it ; taking offsets likewise to the 
bends or corners of the hedges that are near you. 

Next, fix upon some other suitable place, towards the outside 
of the estate, as a third grand station ; to which, from each 
extremity of the diagonal or main-line, or from two convenient 
points in it, lines must also be run. 

These three lines being laid down, will form one large trian- 
gle ; and in a similar manner, if necessary, on the other side of 
the diagonal or main line, a second triangle may be formed. 

The survey must then be completed by forming smaller trian- 
gles, on the sides of the former ; and measuring such lines as 

o 2 



196 LAND-SURVEYING. (Part V. 

will enable you to obtain the fences of each enclosure, the 
boundaries of rivers, roads, lakes, &c. &c. ; and prove the 
whole work. 



Note 1. — If the estate be of a triangular form, three lines must be run, in 
the most convenient manner, so as to form the largest triangle possible ; after 
which, other lines must be measured, offsets taken, &c. &c. ; so that ail the 
fences may be obtained, and the survey completed, as in Plate VIII. 

2. — When an estate is divided into two triangles, it is generally best to 
finish one of them before you measure any of the internal lines of the other, 
as in Plate III. Sometimes, however, it is more convenient and expeditious 
to run some lines in the second triangle before you have finished the first, 
as in Plate X. 

3. — Estates similar to those ha Plates III. and VIII., are very easy to sur- 
vey, as they contain no impediments ; but it is otherwise with estates like 
that in Plate X., where the windings of rivers, roads, and fences, make it 
necessary to run a great number of lines in order to obtain a correct plan 
of the whole estate, and the true area of every part. 

4. — In extensive surveys, where two measurers^are employed, it is best to 
consider the estate as divided into two distinct parts by the diagonal or main- 
line. Each Surveyor may then take a part, and make use of the diagonal as 
his base-line ; and measure such other lines as are necessary to complete that 
part of the survey which he undertakes. By this means the lines of one Sur- 
veyor do not become entangled with those of the other ; and the work is more 
expeditiously and more correctly performed, than if both the Surveyors were 
employed on the same side of the main-line. 

5. — It is sometimes advisable to divide a very large estate in the following 
manner : Measure a line across the estate as near to the middle as convenient ; 
and at right-angles to this line, or nearly at right angles, measure another line, 
through the middle of the estate. These two lines being tied together by a 
connecting line measured from one to the other, will divide the estate into 
four parts, all of which may be measured separately by dividing them into 
triangles as before directed ; and taking such dimensions as are necessary 
to complete the survey. This method is a very good one where three or 
four Surveyors are employed in measuring a large lordship, or even where 
one Surveyor only is employed ; for the first two lines being considered as 
out-boundaries, the estate may be measured in four separate parts ; and 
yet the whole will be so well connected by those lines, that it will be as 
easy to plan as a small survey. 



Plate m. 




Part V.) LAND-SURVEYING. 197 

6. — The method of surveying estates by dividing them into triangles, is 
exemplified and illustrated by Plates III. VIII. and X., the last two of which 
are actual surveys. The field-notes belonging to them are given in an en- 
graven Field-Book ; and Plates IX. and XI. are the finished plans. 

7. — No notes are given to Plate III. as they would have occupied too many 
pages of copperplate ; but the directions of all the lines may be easily ascer- 
tained by the following particulars : The first, or main-line, leads from -I- 1 
to 4 8 ; the second line from -I- 8 to 4 10 ; and the third from 4 10 to 4- 1 ; 
which three lines form the first large triangle. The fourth line extends 
from 4- 2 to 4- 15 ; and the fifth from 4 15 to 4 8 ; which two lines and 
part of the main-line form the second large triangle. The sixth line leads 
from 4 9 to 4 1 1 ; the seventh from 4 20 to 4 6 ; the eighth from 4 7 
to 4 22 ; the ninth from 4 21 to 4 4 ; the tenth from 4 24 to 4- 13 ; and 
the eleventh from 4 12 to 4 23 ; which complete the survey of the first 
triangle. The twelfth line extends from 4 5 to 4 17 ; the thirteenth from 
4 25 to the main-line, southward of 4 3 ; the fourteenth from 4 1 to 4 14 ; 
the fifteenth from 4 14 to 4 26 ; the sixteenth from 4 27 to 4 16 ; the 
seventeenth from 4 18 to 4 28 ; and" the eighteenth from 4 28 to 4- 19 ; 
which finish the whole survey. 

8. — The content of the estate may be found in the following manner : 
Measure the Hues upon the plan, and take the necessary offsets, by a scale of 
8 chains to an inch ; and enter the dimensions in a Field-Book. From the 
dimensions thus obtained, draw a plan by a scale of 2 chains to an inch ; 
then straighten the fences as directed in Part IV. or Part V. ; and measure 
diagonals, perpendiculars, &c. from which compute the content of each 
field. The diagonals, perpendiculars, and contents may be entered in a 
Book of Castings, similar to those belonging to Plates VIII. and X. ; and if 
you should not have a scale of 8 chains to an inch, any other scale will do 
just the same for practice. 

9. — Taking the dimensions, &c. as directed in the last note, will be found 
of infinite service to the learner ; as it will tend to make him very expert in 
entering the field-notes, laying down the lines, and casting the contents, 
which are no small acquisitions towards becoming a complete Land-Sur- 
veyor. 

10. — At the particular request of several eminent Land-Surveyors, who 
very much approve of this Work, I have altered the method of entering the 
notes in the engraven Field-Book. In the first edition, the notes were en- 
tered from the right towards the left ; in this edition they are entered from 
the left towards the right. Both methods are practised by different Sur- 
veyors ; but it appears that the latter method is gaining ground. 

o 3 



198 land-surveying. (Part V. 

11. — Some Surveyors represent the crossings of fences by lines drawn 
across the right and left-hand columns of the Field-Book ; and others by 
lines crossing the middle column. The Author prefers the latter method ; 
but every Surveyor will, of course, follow that of which he most approves. 

12. — Many Surveyors enter their notes in a book about four inches and 
a half in breadth, and fourteen or fifteen in length, when open ; and others 
prefer a book about eight or nine inches long, and seven or eight inches 
broad when open. (See the description of the Field-Book, Part II. ; and 
also the engraven Field-Book belonging to Plates VIII. X. and XII.) 



METHOD II. 

Measure a main-line as nearly to one of the out-boun- 
daries of the estate, as the curves in the hedges will permit ; 
noting the crossings of fences, and taking offsets as before 
directed. 

At a convenient distance, measure another main-line parallel 
or nearly parallel to the first line, so that a number of fences 
running in that direction may be obtained ; and from any two 
stations in the first line, measure lines to some station in the 
second main-line, thus forming a triangle ; so will a station in 
the second main-line become determined or fixed. 

From the first main-line to the second, or from the second to 
the first, measure lines in order to obtain all the fences which 
run in that direction. The remainder of the fences of the en- 
closures contained between the first and second main-lines 
being obtained by running lines in the most convenient man- 
ner, you will have completed the dimensions of a portion of the 
estate, which may then be laid down. 

Parallel or nearly parallel to the second main-line, and at a 
proper distance from it, measure a third ; and proceed with the 
internal lines as before, and you will obtain the dimensions of 
another portion of the estate, which may also be laid down. 

Carry on the survey in a similar manner, until you finish it. 



Plate l\ 




Part V.) LAND-SURVEYING, i99 

y 0(e i._This method is illustrated by Plate IV. which displays the chain- 
lines and stations used in taking the survey. The field-notes are not given ; 
but the following particulars exhibit the directions of all the lines: The first 
main-line leads from + 1 to 4- 6 ; the second from 4- 6 to 4- 7 ; and the 
third line or second main-line, from 4- 7 to 4- 16. The fourth line extends 
from + 16 to 4- 1 ; the fifth or tie-line from + 16 to + 2 ; the sixth from 
4- 2 to 4- 14 ; the seventh from 4- 17 to + 18 ; the eighth from 4- 12, through 
4- 18, to 4- 3 ; the ninth from 4- 4 to 4- 10 ; and the tenth line leads from 
4- 8 to 4- 5 ; thu3 all the fences between the first and second main-lines are 
obtained. 

The eleventh line, or third main-line lead=. from 4- 1 9 to 4- 29 ; the twelfth 
from 4- 29 to 4- 16 ; the thirteenth from 4- 29 to 4- 15 ; the fourteenth from 
4- 15 to 4- 28 ; the fifteenth from 4- 26 to 4- 13 ; the sixteenth from 4- 12 to 
4- 25 ; the seventeenth from 4- 23 to 4- 11 ; the ■ + 30 to 

4- 31 ; the nineteenth from 4- 9, through + 31, to 4- 22 ; and the twentieth 
from 4- 7 to 4- 19, which complete the survey between the second and third 
main-lines. 

The twenty-first line, or fourth main-line, extends from 4- 32 to 4- 40 ; the 
twentv-second from 4- 40 to 4- 29 ; the twenty-third from 4- 40 to 4- 28 ; the 
twenty-fourth from 4- 28 to 4- 38 ; the twenty-fifth from 4- 37 to 4- 27 ; the 
twenty-sixth from + 34 to 4- -36 ; the r .th from 4- 35 to 4- 23 ; the 

twentv-eighth from 4- 34 to 4- 21 ; the twenty-ninth from 4- 20 to 4- 23 ; the 
thirtieth from 4- 32 to + 19, which finish the whole estate. 

2. — In order to practise the learner, a Field-Book may be formed, and 
the content of the estate found in the same manner as directed in Note 8, 
Mothod I. 

3. — Some writers on Surveying instruct their pupils to measure main, 
lines through the estate to be surveyed ; and upon these, by the help of a 
cross, to erect perpendiculars to the opposite angles, and curved fences ; and 
upon these perpendiculars, again, if necessary, to erect other perpendicu- 
1 ars ; thus dividing the whole estate into right-angled triaDgles and trapezoids. 

The method here described is extremely tedious, as many of the perpen- 
diculars will be 12 or 15 chains in length, when the fields are large ; and 
where the fences are much curved, it becomes almost impracticable, ir. 
sequence of the great number of offsets or perpendiculars that must be 
taken, in order to obtain a correct plan of the estate- 

Besides, when the fence to which perpendiculars must be erected, is at a 
considerable distance from the base-line, it will be necessary for an ass:- 

alk along, by the fence, in order to point out to the Surveyor, the ar _ 
and curves to which offsets ought to be taken: and if there be a crooked 
fence on each side of the base-line, two extra helpers will be necessary, if 
the Surveyor intends to perform his work with expedition. Hence we see 
that this process of measuring, not only subjects the Surveyor to a great 
deal of extra trouble, but also to a very considerable, unnecessary expense. 

4 



200 land-surveying. (Part V. 

This method I have never followed in measuring estates ; neither have I 
ever seen it followed by any experienced Surveyor. On the contrary, all 
with whom I am acquainted, consider it quite preposterous. 



METHOD III. 

An estate of four sides may frequently be conveniently sur- 
veyed as follows : Measure four lines in such a manner that 
offsets or insets may be taken to the four out-boundaries of the 
estate ; and tie the first and fourth lines together by a diagonal 
or tie-line measured from one to the other, at the distance of 
five, six, or more chains from the angular point, according to 
extent of the survey ; thus you will be enabled to lay down the 
first four lines, and also the out-boundaries of the estate. 

Next proceed to obtain the internal fences, by measuring lines 
in the most convenient manner ; some of which must be run 
from the first to the third, or from the second to the fourth line, 
or in some other proper direction, so that they may become 
proofs and fast-lines, into which other lines may be run with 
propriety. 

In thus proceeding, it is evident that a great deal will always 
depend upon the dexterity and ingenuity of the Surveyor, as 
no directions can be given that will suit every particular case to 
be met with in practice. 

Note. — This method of surveying an estate, is exemplified by Plate XII. 
the field-notes of which are contained in the engraven Field-Book, given 
with this Work. It is also illustrated in my Mensuration, by Plate III. 
which is the plan of an estate lying in the Township of Farnley, in the 
Parish of Leeds. With this plan there is likewise given an engraven Field- 
Book, and also a book of dimensions, castings, and areas. 

METHOD IV. 

The method which I here intend to describe, is a compound 
of all the foregoing methods of surveying with the chain ; for as 
there are never two estates to be met with which are exactly 
alike, sometimes one method claims the preference, and some- 
times another; but a skilful Surveyor will always adopt that 
by which he can take his dimensions and proofs with the 
greatest accuracy, by the fewest lines. 



Part V.) LAND-SURVEYING. 201 

If an estate be in the form of an irregular .polygon of five, 
six, or more sides, and*" the fences very crooked, such an estate 
may generally be most easily surveyed by dividing it into tri- 
angles, as in Method I. ; but if many of the fences of the dif- 
ferent enclosures run a considerable way in the same direction, 
and the fields in general pretty neat trapeziums, it is commonly 
more eligible to proceed as directed in Method II. 

Sometimes an estate varies so much in its shape, that all the 
methods before described may be used with propriety and ad- 
vantage ; and it frequently happens that an ingenious Sur- 
veyor adopts methods, in particular cases, entirely new to him- 
self; care, however, must always be taken to make one line 
depend upon another, throughout the whole survey, so that 
when you come to lay it down, you may find no lines whose 
positions are undetermined. 

Note 1. — Whatever method of surveying is adopted, the field-notes must 
be entered in a similar manner to those given in the engraven Field-Book. 
Some Surveyors place the letter S, against straight fences, in the Field- 
Book, to distinguish them from those that are crooked ; but they may be 
very well denoted by drawing straight, or crooked lines, as the case requires. 

2. — The estates given in this Work, as examples, are not very extensive, 
in consequence of the serious expense that attends large plates, and the 
great inconvenience of folding them in books ; but it may be remarked, 
that the foregoing methods of surveying are applicable to estates of all 
sizes ; even to those of many thousand acres. 



MISCELLANEOUS INSTRUCTIONS. 

1. When you have *an estate to survey, never begin your 
work too hastily. Walk over the estate ; examine it minutely ; 
and observe by which of the foregoing methods it can be most 
easily measured. Next determine upon that point at which it 
will be most convenient to begin ; and never omit to take 
the range of the first line with a compass. If you do, it will 
be impossible for you to lay it down, in its true position, upon 
the plan. 



202 LAND-SURVEYING. (Part V. 

2. In measuring your main, or any other chain-line, put down 
stations at every place to which you apprehend it may be ne- 
cessary to run lines, in order to complete the surrey. 

3. You may sometimes put down a station, whether you see 
any particular use for it or not ; because it may become ser- 
viceable in correcting an error, should one be committed ; and, 
if it be not used, it will be immaterial. 

4. In measuring your internal lines, it will give you the least 
trouble to run them from one station to another, if you can make 
it convenient ; if not, you must run them from, and continue 
them to some chain-line, and measure the distance upon that 
line, to the nearest station, which may be entered in the field- 
book, thus; run upon 1 line, 30 links S. of -f- 1, &c. 

5. The place where you run upon, or cross a chain-line, may 
be easily ascertained by setting up poles at two of the nearest 
stations in that line ; the crossing will be at the place where 
you are in a direct line with these poles, which may be repre- 
sented by marks cut in the ground, pointing out the directions 
of the lines. 

6. In ranging the poles, there must be one fixed at the station 
from which you intend to depart, and another at the place to- 
ward which you direct your line, if there be no natural mark, 
as a tree, the corner of a house, &c. Then, in a straight line 
with these marks, put down poles at the distance of 4, 6, or 10 
chains from each other, accordingly as impediments may render 
them necessary. 

7. When you are measuring a line across a valley, you must 
proceed forward until you are likely to lose sight of the station 
to which you are going ; then, let your assistant take a pole to 
the other side of the valley, and direct him to place it exactly 
in the line which you are measuring, s^o as to be seen from the 
bottom of the valley ; to this you may continue your line, and 
thence to the end. 

8. "When the stations between which you wish to run a line, 
are so far distant that you cannot see from one of them to the 
other, or when your view is obstructed by an elevation between 
them, you must then, accompanied by your assistant, go to the 
place whence you can distinctly see both ; and turning face to 



Part V.) LAND-SUllVEYING. 203 

face, at a little distance, direct each other to the right or left, 
until you are both in a right line with the stations ; then, one 
of you putting down a pole, the line will be correctly found. 
If the line, however, be so long, that you cannot possibly find 
it by the above methods, it must be ranged at random ; but, 
in this case, you should be extremely careful that your pole 
ranger keeps one pole in a direct line with another, which he 
may accurately effect by always having, at least, two behind 
him. 

9. In measuring a line which passes over a hill, you must 
attend to the directions given in Part IV. in the Method of 
measuring Hilly Ground; but' you will not always find your 
lines to meet correctly, in surveying mountainous estates. 

10. When a river runs through the estate, it will be necessary 
to continue some of your lines across the river, in order to tie 
the whole survey together. 

1 1 . Rivers, large brooks, public roads, and common sewers, 
shall not be included in the area, but only delineated upon 
the plan. If however, their areas be required, they should be 
given separately. 

12. Marshes, bogs, heaths, rocks, &c. belonging to the estate, 
should be distinctly represented upon the plan ; and their mea- 
surements separately returned. 

13. You will generally have an opportunity of representing 
some part of each hedge in your field-book ; and you may de- 
note on which side of the ditch the fence stands, by drawing 
a small bush, or by specifying it in writing. 

14. In surveying estates, the crossings of fences must be 
taken at the outer extremities of the ditches, and not at the roots 
of the quickwood ; because the ditch, and not the fence, is the 
division line between* adjoining fields; but in measuring enclo- 
sures which are separated by walls, the case is generally dif- 
ferent, as the walls most commonly form the lines of division. 
It may also be observed, that the ground upon which a wall 
stands must be measured with the field to which the fence be- 
longs, and as walls are generally broader at the bottom than 
at the top, it is necessary to attend to this circumstance in 
taking the dimensions. 



204 LAND-SUHVEYIXG. (Part V. 

15. When the Surveyor finds it convenient, lie may put down 
stations at the outer extremities of the ditches ; and in planning, 
these stations will, of course, fall upon the black lines, because 
they always represent the boundaries between adjoining fields. 
This accounts for several of the stations appearing on the black 
lines, of the rough plans, in Plate VIIL X. and XII. 

16. In taking a survey, you must enter in your field-book 
the name of each field, or of its proprietor or occupier ; or you 
may make such remarks, as will enable you to distinguish the 
fields from each other, &c. and after the plan is drawn, acquire, 
from persons acquainted with the estate, every necessary addi- 
tional information. 

17. When hedges obstruct your sight, in running the lines, 
it will be necessary to cut down part of their tops, in order to 
see the poles. 

18. If it should happen that you measure a line for which 
you have no particular use, it will serve as an additional proof : 
it is evident that you had better measure too many lines than 
too few. 

19. In taking a survey, you ought to observe to whom the 
adjoining ground belongs ; and specify the same upon the 
plam 

20. Some of our Practical Surveyors use only nine arrows. 
When the leader has advanced ten chains, the follower goes up 
to him, and places his foot or offset-staff at the end of the chain, 
instead of the tenth arrow ; but in this method I do not per- 
ceive any particular advantage. 



GENERAL RULES FOR PL ANNINGLARGE SURVEYS. 

The method of laying down a large survey, from the field- 
book, may easily be acquired by practice ; but as the least ap- 
pearance of difficulty generally discourages a learner, it is pre- 
sumed that the following directions may be found acceptable. 

Having provided a sheet of drawing-paper of a proper size, 
trace with a pencil, a meridian, or north and south line, in such 



Part V.) LAND-SURVEYING. 205 

a manner that your first station may be in some convenient point 
in this line. Then, from your first station, draw your first or 
main-line, making its proper angle with the meridian line, 
which you may then take out with Indian rubber. 

Next, take separately in your compasses, your second and 
third lines, or any two more convenient ones, forming a triangle 
with the main-line ; and placing one foot of your compasses in 
the proper centres respectively, describe arcs intersecting each 
other. Thus will you have three points, from which to form 
a triangle. 

In the same manner proceed with each triangle formed upon 
the main-line, (or upon any other line,) proving your work as 
you advance, until all the triangles are laid down ; and if you 
find all your lines correctly meet, it will be an infallible proof 
of the accuracy of the work. 

The chain-lines being thus laid down, next prick off the 
crossings of fences, and draw lines in their proper situations, 
from one crossing to another, to represent the straight fences. 

The curved fences must be formed by laying down the offsets, 
as already directed. 

When the whole survey is planned, all the fences must be 
drawn with Indian ink, the chain-lines and offsets dotted, and 
the stations, gates, stiles, &c. marked in their proper places : 
the sheet will then represent what is called a " Rough Plan." 

Note 1. — When a fence represents a chain-line, it must not be dotted. 

2.— Practical Surveyors never dot their chain-lines or offsets, but only 
mark their stations upon the plan ; but it is more satisfactory to a learner, to 
be able to see all his chain-lines at a single view. 

3. — In taking a very large survey, it is necessary that the work be laid 
down, and proved every night ; for if an error be committed, and the survey 
continued two or three days before it be discovered, the detection, in the field, 
will probably be attended with a great deal of trouble. 

4. — In laying down large surveys, it sometimes happens that one sheet of 
paper will not contain the whole ; in this case, two or more, must be pasted 
together. 

5. — When you have to lay down a line exceeding the length of your scale, 
draw a line with your pencil, in some convenient place upon the plan ; and 



206 LAND-SURVEYING-. (Part V. 

upon it, at two or more operations, prick off" the distance in question, which 
you may then take in your compasses. 

6. — " Beam compasses, which are very useful in drawing large circles, 
taking great extents, &c. consist of a long straight beam or bar, carrying two 
brass cursors ; one of them fixed at one end, the other sliding alongthe beam, 
with a screw to fasten it on occasionally. To the cursors may be screwed 
points of any kind, as of steel, pencils, &c. To the fixed cursor is sometimes 
applied an adjusting or micrometer screw, by which an extent maybe obtained 
to a very great nicety." — See Hutton's Mathematical Dictionary, I. 315. 



DIRECTIONS FOR PLANNING 
THE ESTATE IN PLATE VIII. FROM THE DIMEN- 
SIONS IN THE ENGRAVEN FIELD-BOOK. 

It appears by the first page of the field-book, that the range 
of the first line is N. N. W. ; and by referring to the compass, 
Plate I. we find that the angle which this line makes with the 
meridian line, is 22° 30'. 

By Prob. 23, Part I. lay down a line making an angle of 
22° 30' which the meridian line ; and by a scale of four chains 
to an inch, prick off 2802 links, from cross or station (-[-) 1, to 
-J- 3 ; and you will thus have the part of the first line. 

Now, as the third line could not be run to + 1, in conse- 
quence of a large quickwood hedge intervening too far to be 
cut down ; it was necessary to produce the first line 30 links 
southward, in order that the first three lines might form a trian- 
gle; consequently, the first line must be continued 30 links 
southward from -j- 1 , in laying down the plan ; and this con- 
tinuation completes tbe first line. 

Take the second line, 3075 links, in your compasses, and 
with one foot in -\~ 3, describe an arc ; and with 3270 links, 
the third line in your compasses, and one foot in a point 30 
links south of -{- 1, describe another arc, intersecting the former 
in + 6 ; join these three points hj drawing lines from -j- 3 to 
+ 6, and from -j- 6 to the above-named point ; and you will 
thus form the triangle 1, 3, 6. 



Part V.) land-surveying. 207 

Next, prick off stations 2, 4, 5, 7, and 8 ; and lay your 
plotting-scale from -f 2 to -f 8, and if it measure 1046, as in 
the field-book, line six, you Lave good reason to conclude tliat 
your dimensions are thus far correctly taken and laid down. 

Also, mark off -f 10, try its distance from -f- 4 ; likewise 
examine the distance from -4-5 to + 7 ; and if you find both 
these lines the same as in the field-book, your survey is evi- 
dently correct. 

With the fourth line, 257, in your compasses, and one foot 
in -4- 1, describe an arc; and with the fifth line, 1004, as a 
radius, and -j- 2, as a centre, make another arc cutting the 
former in + 9 ; hence you have three points by which to form 
the triangle 1, 9, 2. 

Lastly, complete the rough plan by pricking off, and drawing 
all the straight fences; laying down the offsets; making the 
gates ; numbering the fields, &c. &c, as in the Plate. 



DIRECTIONS FOR PLANNING 

THE ESTATE IN PLATE X. FROM THE DIMENSIONS 

IN THE ENGRAVEN FIELD-BOOK. 

We find from the fourth page of the field-book, that the first 
line ranges W. b. N. \ W., making an angle with the meridian 
line, 84° 22£'. 

By Prob. 23, Part I. draw aline, making an angle of 84° 22^' 
with the meridian line ; and by a scale of four chains to an 
inch, prick off 5445 links, from -j- 1 to + 12; and you will 
thus obtain the first line ; upon which prick off stations 2, 3, 
4, 5, 6, 7, 8, 9, 10, and 11. 

With 900, part off the third line, in your compasses, and -f 1, 
as a centre, describe an arc ; and with 625, the fourth line, 
as a radius, and one foot in -f 2, intersect the former arc in 
-f 22. From -f 2, draw a line to -j- 22 ; and from -f 1, 
through -f 22, draw the third line, equal to 1360, and you 
will obtain + 23. 



208 land-surveying. (Part V. 

With the second line, 3790, in your compasses, and + 12, 
as a centre, describe an arc ; and with 925, part off the fifth 
line, as a radius, and -f- 23, as a centre, describe another arc, 
cutting the former in + 21. From + 23, through + 21, draw 
a line equal to 2090, and you will thus obtain the fifth line, and 
also stations 24, 25, and 20. 

Draw a line from + 12 to + 21, and you will have the 
second line; and also stations 13, 14, 15, 16, 17, 18, 19, and 
20; and draw another from + 2G, to a point in the first line, 
295 "W. of + 10 ; and you will obtain the sixth line ; and like- 
wise stations 27 and 28. 

With 2325, the twenty -sixth line, in your compasses, and + 3 
as a centre, describe an arc; and with 1210, part of the twenty- 
seventh line, as a radius, and one foot on the first line, 150, 
-yy. of + 7, describe another arc, cutting the former in + 33. 
Draw a line from + 3 to + 33 ; and from + 33, through the 
intersection of the first line, draw the twenty-seventh line, equal 
to 2040, and you will obtain + 43. 

Next, with 446, the seventh line, in your compasses, and + 
12, as a centre, describe an arc; and with 2528, the eighth line, 
as a radius, and + 33, as a centre, describe another arc, cutting 
the former in + 29. Draw lines from + 12 to + 29, and 
from + 29 to + 33, and you will obtain stations 30, 31, and 
32 ; and also draw the ninth line from + 32, through + 8, and 
_j_ 1 6, to + 27, and you will have stations 34, 35, 36, and 37. 

Join stations 11 and 13, and you will obtain the 10th line ; 
28 and 30, and you will have the 11th line; 37 and 18, and 
you will obtain the 12th line; 19 and 25, and you will have 
the 13th line; 38 and 20, and you will obtain the 14th line; 
20 and 39, and you will have the 15th line; 24 and 39, and you 
will obtain the 16th line; 39 and 19, and you will have the 
17th line; 17 and 27, and you will obtain the 18th line. 

From + 31, through + 9, draw the 20th line, equal to 1175, 
and you will obtain stations 40 and 41 ; join 36 and 40, and 
you will have the 19th line; and from + 41, through + 34, 
draw a line to a point in the 1st line, 72 E. of + 7, and you 
will obtain the 21st line. 

Draw a line from + 35 to + 43, and you will have + 42, 



Part V.) LAND-SURVEYING. 209 

and the 23rd line ; and join -f 42 and 36, and you will 
obtain the 22nd line. Draw a line from + 23 to the first line, 
115 E. of + 5, and you will obtain + 45, and the 29th line; 
from -f 43 to -f 45, and you will have -f 44, and the 24th 
line ; from -j- 3 to -f 45, and you will obtain the 25th line. 

Lastly, complete the rough plan, by pricking off, and drawing 
all the straight fences ; laying down the offsets ; making the 
gates ; forming the bases of buildings ; shading the river ; 
numbering the fields ; &c. &c. as in the Plate. 

Note 1. — Hot-pressed drawing-paper is best for plans, because its surface 
is very smooth ; consequently, fine lines maybe drawn upon it. Parchment 
and vellum are more durable than paper ; hence they are generally used for 
planning estates belonging to gentlemen who are desirous that the plans may 
be handed down to their posterity. Vellum exceeds parchment in durability ; 
and it may be necessary to remark, that when either of them is used for plan- 
ning, it must first be rubbed with clean flannel dipped in the best Paris 
whiting. This operation clears its surface from grease ; and facilitates the 
movements of the pen. 

2. — In damp weather, paper expands, and in dry weather, it contracts ; 
consequently, if a plan be drawn when the paper is in a moist state, and the 
content be not found till after it has become perfectly dry, the diagonals and 
perpendiculars will measure too little, and will of course give the area too 
little also ; but if the plan be drawn when the paper is dry, and the area be 
found after it has expanded by a change in the atmosphere, the diagonals 
and perpendiculars will measure too much, and will consequently give the 
area too much likewise. Hence the necessity of having the paper in the same 
state of temperature when you find the area, that it was in when you laid 
down the chain-lines, offsets, &c. 

3. — The most expeditious method of laying down crooked fences, is by 
means of an offset-scale, which must be used with the plotting-scale in the 
following manner : Lay one edge of the plotting-scale close by the base-line, 
and bring the end of the offset-scale in contact with the edge of the plotting- 
scale, so that the edges of the scales may form a right-angle ; then by the 
edge of the offset-scale, prick off, in its proper situation, the first offset, with 
a pencil finely pointed. Keep the plotting-scale firm, and slide the offset-scale 
to the place of the next perpendicular, which prick oft' as before ; and thus 
proceed until all the offsets are finished. 

4. — Bi-ooknian and Langdon's prepared lead pencils, of different degrees 
of hardness, for the iw of Engineers, Architects, Land-Surveyors, and Artists, 

P 



210 LAND-SURVEYING. (Part V. 

are now in high repute among Draftsmen. The pencils marked H. H. very 
hard, and H. not quite so hard, are well adapted for the use of Land-Sur- 
veyors ; as they bear pointing better than any other ; and produce much finer 
lines. 



TO COMPUTE THE CONTENTS. 

After the -whole survey is laid down, Practical Surveyors 
straighten the crooked fences of each field, as directed in Part 
IV. ; and then divide the fields into trapeziums and triangles, 
and take such dimensions, by the scale, as are necessary to find 
the separate area of each field. They then collect all the areas 
into one sum ; afterward find the area of the whole survey, as 
if it were a single field, and if it appears to be equal, or nearly 
equal, to the sum of the separate areas, previously found, they 
justly infer that their survey is correct. 

Note 1 .—Those who do not approve of finding the area by the method of 
casting, may make use of the offsets taken in the survey, where convenient ; 
and if more be wanted, they may be measured by the scale ; for in measuring 
a number of small parts by it, some will probahly be taken a little too large, 
and others a little too small, so that, in the end, they will nearly counter- 
balance each other. 

2. — Practical Surveyors generally lay down their lines by a scaleof 4 chains 
to an inch, when their surveys are very large ; and in computing the contents, 
they measure the bases and diagonals by the same scale, but the perpendi- 
culars by a scale of 2 chains to an inch ; consequently, the product of the base 
and perpendicular of a triangle, will be its area. To treat small surveys, in a 
similar manner, by a scale of 2 chains, and of 1 chain to an inch, must, of 
course, be very correct. 

3. — When the survey is not very large, the content of each field may be 
set down in some convenient place upon the plan. In other cases, it may be 
entered within the field itself. Some gentlemen, however, prefer having the 
areas of their estates given in a book of particulars, containing numbers, or 
letters of reference, corresponding to those upon the plan. 

4. — As some Surveyors prefer a parallel ruler to a lanternhorn, or abowof 
whale-bone and silk, for reducing crooked fences to straight ones, I have in . 
the following Problems, given the method of using that instrument, in order 
that this work may meet the approbation of all classes of scientific readers ; 
and be rendered as useful and practical as possible. 



Part V.) LAND-SURVEYING. 211 

5. When there are no dimensions given in the following Problems, the 

figures may be measured by a scale, and then laid down in the learner's 
book ; after which, the operations by the parallel ruler may be performed. 
Or, for practice, figures may be made at pleasure ; and the necessary equa- 
lising lines drawn, according to the subsequent directions. 



THE USE OF THE PARALLEL RULER 

IN REDUCING CROOKED FENCES TO STRAIGHT 

ONES, IN ORDER TO FIND THE AREAS OF 

FIELDS BY THE METHOD OF CASTING. 



PROBLEM I. 

To draw a right Line A D,from the Point A, through the Line 
B (7, so that the Quantities on each Side of the Line A D, 
may be equal. 

E 




Draw, with your pencil, a temporary line C E, at pleasure ; 
then your ruler being closed, lay it from C to A ; hold the side, 
that is next to you, fast ; open the other to B ; make a mark 
with your pencil upon the temporary line C E, where the edge 
of the ruler cuts that line, as at D ; draw a line from A to D, 
and the quantities on each side of this line will be equal ; that 
is, the triangle A B F will be equal to the triangle CDF. 

p 2 



212 land-surveying. (Part V. 



DEMONSTRATION. 

Draw the line A C, and also the line B D, which is evidently 
parallel toA C; then by Theo. 6, Part I. the triangle ABC 
is equal to the triangle ACD; take away the triangle A C F, 
which is common to both, and there remains the triangle A B F 
equal to the triangle CDF. 

Note 1 . — The solutions of all the following Problems are founded upon the 
foregoing demonstration. 

2. — If it had been required to draw the equalising line from the angle 
C, through the line A B, the temporary line must have been made from the 
angle A. 

3. — All the operations must be performed with the utmost care and accu- 
racy ; and if, at any time, the ruler be suffered to slip, the work must be 
repeated, or it will not be correct. 

4. — When an error has been committed, it may frequently be discovered 
by the eye, after the equalising line is drawn. 



PROBLEM II. 

Let the irregular figure A B C D E A represent an Offset taken 
in surveying a Field; it is required to draw a right Line from 
the Angle A, so as to reduce the Figure to a right-angled 
Triangle. 




Produce the perpendicular B C, for a temporary line. 

Lay your ruler from C to E; bring it down in a parallel 



Part V.) LAND-SURVEYING. 213 

position to D ; and make a mark upon the line B C, where 
the edge of the ruler intersects that line, as at m. 

Lay jour ruler from m to A ; move it in a parallel direction 
to E ; and make a mark upon the line B C, close by the edge 
of the ruler, as at F. 

Draw a line from Ato F; and the triangle A B F will be 
equal to the irregular figure A B C D E A ; hence the area 
may be found by multiplying the base A B, by half the per- 
pendicular B F. 

Note 1. — In practical operations, the equalising and temporary lines must 
be made with a pencil finely pointed ; and effaced with Indian rubber, 
after the area is found. 

2. — If perpendiculars be let fall from the angles E and D, upon the 
base A B ; the necessary dimensions taken by a scale ; and the area of the 
irregular figure A B C D E A obtained by the rules for triangles and 
trapezoids, it will be found equal to the area of the right-angled triangle 
ABF; great care, however, must be used to make the lines very fine, 
and to take the dimensions of all the figures with the utmost accuracy. 



PROBLEM III. 



It is required to reduce the Offset 1, 2, 3, 4, 5, to a right-angled 
Triangle, hy drawing an equalising Line from the fifth Angle, 
through the irregular Fences, 




214 land-surveying. (Part V. 

Perpendicularly to the base, and from the first angle, draw 
a temporary line. 

Lay your ruler from the first to the third angle ; move it in 
a parallel position to the second angle ; and mark the tempo- 
rary line at number 1. 

Lay your ruler from number 1, to the fourth angle ; bring it 
down in a parallel direction to the third angle ; and mark the 
temporary line at number 2. 

Lay the ruler from number 2, to the fifth angle ; move it 
parallel to the fourth angle ; and mark the temporary line at 
number 3. 

Draw a line from the fifth angle to number 3 ; and 5, 1, 3, 
will be the right-angled triangle required ; hence the area of 
the irregular offset may be found by multiplying the base 1, 5, 
by half the perpendicular 1, 3. 



PROBLEM IV. 



It is required to lay down a right-line Offset* from the following 
Dimensions ; to reduce it to a Scalene Triangle ly the Parallel 
Ruler ; and to find its Area loth ly the Method of Offsets and 
Casting. 





300K 
100 G 
200 E 
150 C 

"West 





AL 




1500 


H 


1100 


F 


800 


D 


500 


B 


100 




000 


From 


A, go 



Part V.) 



LAND-SURVEYING. 



215 




Having laid down the figure ; produce the side A C, at 
pleasure, for a temporary line. 

Lay the ruler from the first angle A, to the third angle E ; 
move it parallel to the second angle C ; and mark the temporary 
line at 1, which, in this case, is at the second angle, because the 
said A C, is the temporary line. 

Lay the ruler from 1, to the fourth angle G ; move it parallel 
to the third angle E ; and mark the temporary line at 2. 

Lay the ruler from 2, to the fifth angle K ; move it parallel 
to the fourth angle, G ; and mark the temporary line at 3. 

Lay the ruler from 3, to the sixth angle L ; move it parallel 
to the fifth angle K ; and mark the temporary line at 4. 

Draw a line from the sixth angle L, to number 4 (M) ; and 
A L M will be the scalene triangle required. 



Computation of the Area by Offsets. 

Here 150 X 100 = 15000, twice the area of the triangle 

ABC; 150 + 200 x 400 = 350 X 400 = 140000, twice 

the area of the trapezoid B D E C ; 200 -f 100 X 300 = 300 

X 300 = 90000, twice the area of the trapezoid DFGE; 

100-1- 300 X 300 = 400 X 300 = 120000, twice the area of 

the trapezoid FHKG; and 400 X 300 = 120000, twice the 

area of the triangle HLK; then 15000 -f 140000 + 90000 

-f 120000 -f- 120000 = 485000, twice the area of the whole 

offset ; and 485000 ~ 2 = 242500 square links = 2a. 1r. 28p. 

the area required. 

p 4 



216 



LAXD-SURVEYING. 



(Part V. 



Computation of the Area by Casting. 

From the angle M, let fall the perpendicular M N, which you 

•11 £ j , «« i. , i 323 X 1500 484500 

will find to measure 323 links; then — — 

2 2 

242250 square links = 2a. 1r. 27.6p. the area required; which 

differs only four-tenths of a perch from the area found by 

offsets. 



PROBLEM V. 

Lay down a curve-line Offset from the following Dimensions ; re- 
duce it to a right-angled Triangle by the Parallel Rider ; and 
find its Area both by equidistant Ordinates and Casting. 





AN 





1200 


M 190 


1000 


K 260 


800 


G 270 


600 


E 250 


400 


C 180 


200 ' 





000 


From 


A > g° 







L 
H 
F 
D 
B 

East. 




Having laid down the figure, erect the perpendicular A P, 
for a temporary line. 



Part V.) LAND-SURVEYING. c 2l7 

Lay the ruler from A to E ; move it parallel to C ; and mark 
the temporary line at 1. 

Lay the ruler from 1 to G ; move it parallel to E ; and mark 
the temporary line at 2. 

Lay the ruler from 2 to K ; move it parallel to G ; and mark 
the temporary line at 3. 

Lay the ruler from 3 to M; move it parallel to K ; and 
mark the temporary line at 4. 

Lay the ruler from 4 to N ; move it parallel to M ; and mark 
the temporary line at 5. 

Draw a line from N to 5 (P) ; and NAP, will be the right- 
angled triangle required. 



Computation of the Area by equidistant Ordinates. See Prob. 9, 
Part III 

Here the sum of the first and last ordinates is nothing; (J 80 
+ 270 -f 190) X 4 = 640 X 4 = 2560, four times the sum of 
the even ordinates; and (250 -f- 260) X 2 = 510 x 2 = 1020, 

*^ A « A ~1J JT ' « A 2560 + 1020 + 200 

twice the sum ot the odd ordinates ; then 

3 

3580x200 716000 nn nnn 

= — = 238666 square links = 2a. 1r. 21. 8p. 



3 
the area required. 



Computation of the Area by Casting, 

Measure the perpendicular A P, which you will find to be 

,. , . 398x1200 477600 
398 links ; then = -= 238800 square links = 

2a. 1r. 22p. the area required; which differs only two-tenths 
of a perch from that found by equidistant ordinates. 

Note. — When a curve-line offset is to be reduced to a triangle by the parallel 
ruler, a competent number of points must be assumed in the curve, to denote 
angles. These points must be taken at such distances from each other, that 
a right line drawn between any two adjacent points, would nearly coincide 
with the curve. 



Q1Q 

LAXD-SURVEYIXG. ( p art y 



PROBLEM VI. 



It is required to reduce the following curve-line Offset to a right- 
angled Triangle by the Parallel Ruler. 




Erect a perpendicular at one end of the base, for a temporary 
line ; and assume a competent number of points in tbe curve 
to denote angles. 

Lay the ruler from 1 to 3 ; move it parallel to 2 ; and mark 
the temporary line at 1. 

Lay the ruler from 1 to 4 ; move it parallel to 3 ; and mark 
the temporary line at 2. 

Lay the ruler from 2 to 5 ; move it parallel to 4 ; and mark 
the temporary line at 3. 

Lay the ruler from 3 to 6 ; move it parallel to 5 ; and mark 
the temporary line at 4. 

Lay the ruler from 4 to 7 ; move it parallel to 6 ; and mark 
the temporary line at 5. 

Lay the ruler from 5 to 8 ; move it parallel to 7 ; and mark 
the temporary line at 6. 

Draw a line from 8 to 6 ; and 8, 1, 6, is the triangle required ; 
hence the area of the irregular offset may be found by multi- 
plying the base 1, 8, by half the perpendicular I, 6. 



Part V.) 



LAND-SUllVEYING. 



219 



PROBLEM VII. 

It is required to reduce the irregular Figure A B C D E F G 
H K,toa Triangle, by the Parallel Ruler. 




1 A 3 2 



Produce the base A B, both ways, at pleasure, for a tem- 
porary line. 

Lay the ruler from A to H ; move it parallel to K ; and 
mark the temporary line at 1. 

Lay the ruler from 1 to G; move it parallel to H ; and mark 
the temporary line at 2. 

Lay the ruler from 2 to F ; move it parallel to G ; and mark 
the temporary line at 3. 

Draw a line from F to 3 ; and it will be a side of the re- 
quired triangle. 

Again, lay the ruler from B to D; move it parallel to C ; 
and mark the temporary line at 1. 

Lay the ruler from 1 to E ; move it parallel to D ; and mark 
the temporary line at 2. 



220 land-surveying. (Part V. 

Lay the ruler from 2 to F ; move it parallel to E ; and mark 
the temporary line at 3. 

Draw a line from F to 3 ; and 3 F 3 will be the triangle 
required ; hence the area of the irregular figure A B C D E F 
G H K, may be found by multiplying the base 3, 3, by half 
the perpendicular F m. 

Note. — The method of reducing fields of four or five sides, to triangles of 
equal areas, may be seen in Problems 16 and 17, Part L 



PROBLEM VIIL 

It is required to reduce the irregular Figure A B C D E F G 
H K L M JV, to a Triangle, by the Parallel Ruler. 



V 




Draw the temporary line 1, 2, to touch the angle A. 



Part V.) LAND-SURVEYING. 221 

Lay the ruler from A to C ; move it parallel to B ; and mark 
the temporary line at 1. 

Lay the ruler from 1 to D ; move it parallel to C ; and mark 
the temporary line at 2. 

Lay the ruler from 2 to E ; move it parallel to D ; and mark 
the temporary line at 3. 

Draw a line from E to 3 ; and produce it at pleasure, for a 
temporary line. 

Lay the ruler from 3 to M ; move it parallel to N ; and mark 
the temporary line at a. 

Lay the ruler from a to L ; move it parallel to M ; and mark 
the temporary line at n. 

Lay the ruler from ntoK; move it parallel to L ; and mark 
the temporary line at m. 

Draw a line from mtoK; and produce it at pleasure, for a 
temporary line. 

Lay the ruler from KtoG; move it parallel to H ; and mark 
the temporary line at 1 . 

Lay the ruler from 1 to F ; move it parallel to G ; and mark 
the temporary line at 2. 

Lay the ruler from 2 to E ; move it parallel to F ; and mark 
the temporary line at 3. 

Draw a line from E to 3 ; and E 3 m, will be the triangle 
required ; hence the area of the irregular figure A B C D E F 
G H K L M N, may be found by multiplying the base E m by 
half the perpendicular 3 x. 



222 



LAND-SURVEYING 



(Part V. 



PROBLEM IX. 

It is required to reduce the irregular Figure A B C D E F G 
H K L M, to a Trapezium, by the Parallel Ruler. 




Produce the line A B, at pleasure, for a temporary line. 

Lay the ruler from A to L ; move it parallel to M ; and mark 
the temporary line at 1 . 

Lay the ruler from 1 to K ; move it parallel to L ; and mark 
the temporary line at 2. 

Draw a line from 2 to K ; and produce it at pleasure, for a 
temporary line. 

Lay the ruler from K to G; move it parallel to H ; and 
mark the temporary line at 3. 

Lay the ruler from 3 to F ; move it parallel to G ; and mark 
the temporary line at 4. 

Lay the ruler from 4 to E ; move it parallel to F ; and mark 
the temporary line at 5. 

Draw a line from 5 to E ; and produce it at pleasure, for a 
temporary line. 



Part V.) LAND-SURVEYING. 223 

Lay the ruler from E to C ; move it parallel to D ; and mark 
the temporary line at 6. 

Lay the ruler from 6 to B ; move it parallel to C ; and mark 
the temporary line at 7. 

Draw a line from 7 to B ; and B, 7, 5, 2, will be the tra- 
pezium required ; hence the area of the irregular figure ABC 
D E F G H K L M, may be found by multiplying the diagonal 
B ,5, by half the sum of the two perpendiculars 7 m and 2 n. 



PROBLEM X. 

It is required to reduce the irregular Figure A B C D E F G H 
K L M N P R, to a Trapezium, by the Parallel Ruler. 




Continue A R, for a temporary line. 

Lay the ruler from A to C ; move it parallel to B ; and mark 
the temporary line at 1 . 

Lay the ruler from 1 to D ; move it parallel to C ; and mark 
the temporary line at 2. 



224 land-surveying. (Part V. 

Draw a line from D to 2 ; and produce 4t at pleasure, for a 
temporary line. 

Lay the ruler from 2 to P ; move it parallel to R ; and mark 
the temporary line at 3. 

Lay the ruler from 3 to X ; more it parallel to P ; and mark 
the temporary line at 4. 

Draw a line from 4 to X ; and produce it at pleasure, for a 
temporary line. 

Lay the ruler from X to L; move it parallel to M; and 
mark the temporary line at .5. 

Lay the ruler from 5 to K; more it parallel to L ; and mark 
the temporary line at 6. 

Lay the ruler from 6 to H ; move it parallel to K ; and mark 
the temporary line at 7. 

Draw a line from 7 to H ; and produce it at pleasure, for a 
temporary line. 

Lay the ruler from H to F ; move it parallel to G ; and mark 
the temporary line at 8. 

Lay the ruler from 8 to E ; move it parallel to F ; and mark 
the temporary line at 9. 

Lav the ruler from 9 to D ; more it parallel to E ; and mark 
the temporary line at T. 

Draw the line D T ; and D T 7, 4, will be the trapezium 
required ; hence the area of the irregular figure may be found 
by multiplying the diagonal D 7, by half the sum of the two 
perpendiculars T m and 4 n. 



Part V.) 



LAND-SURVEYING. 



225 



PROBLEM XI. 

It is required to draw an equalising Line, by the Parallel Ruler, 
through the irregular Fences A B C D E, so that the two Fields 
which they separate, may be reduced to Trapeziums. 




Lay the ruler from A to C ; move it parallel to B ; and mark 
the temporary line K G, at 1. 

Lay the ruler from 1 to D ; move it parallel to C ; and mark 
the temporary line at 2. 

Lay the ruler from 2 to E ; move it parallel to D ; and mark 
the temporary line at 3. 

Draw a line from E to 3 (L) ; and the irregular figure A B 
C D E F G, will he reduced to the trapezium LEF6; and 
the irregular figure A B C D E H K, to the trapezium L E H K ; 
hence their respective areas may be obtained by measuring 
diagonals and perpendiculars. 

Note 1. — Sometimes the proprietors of adjoining estates agree to straighten 
crooked fences or brooks, by giving and taking equal quantities of land. 



226 



LAND-SURVEYING. 



(Part V. 



When this is the case, you must first measure and plan the ground ; then 
draw the equalising line as directed in the last Problem ; and take the dis- 
tance from A to L, very correctly by the scale. Measure this distance in the 
field, from the angle A ; range the division line E L, and takes it out ; and 
the work will be completed. 

2. — It will be advisable to measure, both on the plan and in the field, the 
parts cut off on each side, by the division line, in order to prove the work ; 
for an error committed in dividing land, is of serious consequence, if it be not 
discovered and rectified before the new fence is made. If the discovery takes 
place after the groundhas been fenced off, either the fence must be altered, or 
the land must be valued ; and the person who has had too much awarded to 
him, must pay the balance. 



PROBLEM XII. 

It is required to draw an equalising Line by the Parallel Ruler, 
so that the curved Fence which separates the two Fields in the 
following Figure, may be reduced to a straight Fence. 




Lay the ruler from 1 to 3 ; move it parallel to 2 ; and mark 
the temporary line A B, at 1. 

Lay the ruler from 1 to 4 ; move it parallel to 3 ; and mark 
the temporary line at 2. 



Part V.) LAND-SURVEYING. 227 

Lay the ruler from 2 to 5 ; move it parallel to 4 ; and mark 
the temporary line at 3. 

Lay the ruler from 3 to 6 ; move it parallel to 5 ; and mark 
the temporary line at 4. 

Lay the ruler from 4 to 7 ; move it parallel to 6 ; and mark 
the temporary line at 5. 

Draw a line from 7 to 5, and it will reduce the figure A B 
C D, to two trapeziums ; hence their respective areas may be 
found by measuring diagonals and perpendiculars. 



The following general Rule for the Parallel Ruler, 
will be found of considerable service to learners ; and 
may be easily committed to memory. 



GENERAL RULE. 

1 . Lay the ruler from the first to the third angle ; move it 
parallel to the second angle ; and you will have the first mark 
on the temporary line. 

2. Lay the ruler from the first mark on the temporary line, 
to the fourth angle ; move it parallel to the third angle ; and 
you will have the second mark on the temporary line. 

3. Lay the ruler from the second mark on the temporary line, 
to the fifth angle ; move it parallel to the fourth angle ; and 
you will have the third mark on the temporary line. 

4. Lay the ruler from the third mark on the temporary line, 
to the sixth angle ; move it parallel to the fifth angle ; and you 
will have the fourth mark on the temporary line. 

5. Lay the ruler from the fourth mark on the temporary line, 
to the seventh angle ; move it parallel to the sixth angle ; and 
you will have the fifth mark on the temporary line. 

6. Lay the ruler from the fifth mark on the temporary line, 
to the eighth angle ; move it parallel to the seventh angle ; and 
you will have the sixth mark on the temporary line. 

Q2 



228 LAND-SURVEYING. (Part V. 

7. Lay the ruler from the sixth mark on the temporary line, 
to the ninth angle ; move it parallel to the eighth angle ; and 
you will have the seventh mark on the temporary line. 

8. Lay the ruler from the seventh mark on the temporary 
line, to the tenth angle ; move it parallel to the ninth angle ; 
and you will have the eighth mark on the temporary line, &c. &c. 

Note. — As the operations of the parallel ruler, in straightening crooked 
fences, are founded upon a mathematical truth, it is certainly, in most cases, 
preferable to a lantern horn ; hut in large surveys, where the fences are much 
curved, it will be found that the latter may be applied with much more ex- 
pedition than the former ; and if it be used by a skilful hand, its results 
will be sufficiently correct for general practice. (See Problems I. and II. 
Part IV.) 



A BOOK of DIMENSIONS, CASTINGS, and AREAS, 

Belonging to Plate VIII. 



Names 

of the 

Proprietors. 


i 

H 

S3 
rC| 
■4-a 

C 

© 

ft 


03 

o 

'IP 

5 


<v 

P-< 
<v 

-us 

xn 


& 

© 

© 
© 


03 

P-l 
f-i 

g 

m 


Quantity 

in 
A. Dec. 


Quantity 

in 
A. R. P. 


Mr. Dalton's Close 
Mr. Cayley's Close 
Mr. Whisk ers Close 
Mr. Straker's Close 
Mr. Straker's Close 
Mr. Ellard's Close 


1 

2 
3 

4 

6 


625 

916 

742 

2094 

1855 

2197 


180 

52 

123 

160 
328 
574 


247 
155 
481 
268 


180 
299 
278 
641 
596 
574 


1.12500 

2.73884 

2.06276 

13.42254 

11.05580 

12.61078 


1 

2 

2 

13 

11 
12 



2 

1 

2 


20 
38 
10 

28 

9 

18 


Whole Quantity 


43.01572 


43 





3 









Part V.) LAND-SURVEYING. 229 

Note 1 . — In the first edition of this Work, the content of the estate, in 
Plate VIII. was found from a plan of 2 chains to an inch. The bases, 
diagonals, and perpendiculars, were measured by the scale used in planning ; 
the offsets taken in the field, were used, where convenient ; and when those 
were insufficient, more were measured by the scale. In this edition, the 
crooked fences have been straightened by the Parallel Ruler ; the bases and 
diagonals measured by a scale of 2 chains to an inch ; and the perpendicu- 
lars by a scale of 1 chain to an inch ; hence the area of each triangle was 
found by multiplying the base by the perpendicular, and the area of each 
trapezium by multiplying the diagonal by the sum of the two perpendiculars- 

The diagonals, perpendiculars, and areas are entered in the foregoing 
book of castings ; and it may also be observed that the bases of triangles 
are put down in the column of diagonals, and their perpendiculars, in the 
first column of perpendiculars. (See Notes 1 and 2, Method of computing 
the Contents, Part V.) 

2. — In straightening crooked fences by the Parallel Ruler, it frequently 
happens that one equalising line will serve for two adjoining fields ; and al 
most every irregular figure may be reduced either to a triangle, or a trape- 
zium. (See Problems 16 and 17, Part I. ; and also the Use of the Parallel 
Ruler, Part V.) 



Q3 



230 



LAND-SURVEYING. 



(Part V. 



A BOOK of DIMENSIONS, CASTINGS, and AREAS, 

Belonging to Plate X. 



Names 
of the 
Fields. 



Grime Garth .... 

House Ing 

Sandy Field 

Low Holme 

Brook Close 

Low Close 

Marsh Close 

Green Meadow., 
Horse Pasture . . . 

Cow Pasture 

Calf Garth 

Long Meadow... 

River Close 

Primrose Close . 

Bridge Ing 

Shady Ing 

Hare Park 

Long Tongue . . . 



11166 
2 15814 
31098J196 

4 861*259 

5 1130'215 



Pi 


d 




a> 


03 




p-i 
u 


& 


Quantity 


<u 






Ph 


P-I 




H3 
PI 


O 


in 


O 

o 


1 l 




oq A. Dec. 


95 


360 


4.19760 



Quantity 



A. R. P. 



969 



1209 
846 
741 

962 
725 
1781 
810 
141046 
151733 



875 

880 

1092 



243 
336 
153 
161 
150 



440 

i 

293 

3471 

215 

243 



200 
170 
104 



180133 

2261224 



178 



17,4 



183,210 

287153 
159 18? 



147 

284 



167 



336 
353 
331 
254 
313 
450 
352 
393 
440 
346 
314 
284 



Whole Quantity 67.85070 



6.95640 
3.21714 
2.98767 
2.42950 
2.35467 
4.06224 
2.98638' 
2.45271J 
2.44348, 
2.26925J 
8.01450 
2.85120 
4.11078 
7.62520 
3.02750 
2.76320 
3.10128 



3 38 

1 :32 

1 31 



67 



16 



Note. — In the first edition of this Work, the content of the estate, in Plate 
X. was found from a plan of 2 chains to an inch, by making the crooked 
fences straight by a lantern horn, as directed in Part IV. In this edition all 



Part V.) LAND-SURVEYING. 231 

the crooked fences have been straightened by the Parallel Ruler ; the bases 
and diagonals measured by a scale of 2 chains to an inch, and the perpen- 
diculars by a scale of 1 chain to an inch ; and hence the foregoing Book of 
Dimensions, Castings, and Areas, was formed. 



TO TRANSFER A ROUGH PLAN TO A CLEAN SHEET 
OF PAPER, OR TO A SKIN OF PARCHMENT OR 
VELL UM, IN ORDER TO MAKE A FINISHED PLAN; 
ALSO TO ENLARGE OR REDUCE PLANS, $c. 



METHOD I. 

By Points. 

Having laid the fresh sheet upon a smooth table, lay the 
rough plan upon it ; and with four small nails, (or weights, or 
books,) fasten the corners of both to the table. Then, with your 
pricker, pierce the extremities of straight lines, and as much of 
the curved ones as will enable you to draw them on the new 
plan. Next separate the papers, and trace the outlines and 
fences with a black lead pencil, after which draw them with a 
fine pen and good Indian ink. 

Note. — Common ink ought never to be used in planning, because it not 
only sinks too deep into the paper, but generally, in process of time, be- 
comes discoloured. 



METHOD II. 

By Tracing Paper. 

Take a sheet of writing paper, of the same size as the rough 
plan, and rub one side of it with black lead powder ; then lay 
it upon the sheet which you intend for your new plan, with the 
black side downward ; upon both lay the rough plan, and fasten 

q 4 



232 land-surveying. (Part V. 

them all to the table, as before directed. Next, run your tracer 
gently over all the lines upon the plan, so that the black lead 
under them, may be transferred to the fresh paper. They must 
then be drawn with Indian ink, as before directed. 

Note. — This method of transferring is preferable to the former, because 
it does not injure the plans. 



METHOD III. 

By a Copying Glass. 

A copying glass is a large square, or rectangular piece of the 
best window glass, fixed in a frame of wood, which can be 
raised to any angle, like a desk, the lower side resting upon a 
table ; and a screen of blue paper may be fitted to the upper 
edge, and stand at right angles to it. 

Place this frame at a convenient angle, against a strong light ; 
fix the old plan and clean paper firmly together by pins, the 
clean paper uppermost, and on the face j)f the plan to be copied ; 
lay them with the back of the old plan next the glass, namely, 
that part which you intend to copy first. 

The light through the glass will enable you to perceive dis- 
tinctly every line of the plan upon the clean paper, and you 
can easily trace over them with a pencil ; and having finished 
that part which covers the glass, slide another part over it, and 
copy this, and thus continue till the whole be copied. 

Note.- — Those who have not a copying glass, may use a rectangular piece 
of window glass fixed in a common frame ; and when copying, it may be 
placed in an inclining position, with its top against a window, and its bottom 
upon the window-seat, if it be nearly level with the bottom of the window. 
A pane in a window is not unfreguently used for copying small drawings. 



METHOD IV. 

By similar Squares. 

The three foregoing methods of transferring or copying plans, 
can only be applied, when the rough plan is of the same size 



Part V.) LAND-SURVEYING. 233 

which you wish the finished one to be ; but as it may be ne- 
cessary to reduce the size of the original, this may be done by 
similar squares. 



EXAMPLE. 



Suppose the following inclosures to have been laid down by 
a scale of 2 chains to an inch ; it is required to reduce them to 
one of 4 chains to an inch. 



f . 1 -• ;--_. : 

S\ : j : i : > 


" 1 


. * \ : ," " " "I ' : 




!'■"/ 1 : 11 ; 




i (1 >^h_ ; V 





By a scale of 2 chains to an inch, draw the line AB = 7 
chains. At A and B erect the perpendiculars A D and B C, 
each of which make =. 6 chains ; and join D C. Divide the 
lines A B and D C, each into 7 equal parts ; and the lines A D 
and B C, each into 6 equal parts ; join the opposite points of 
division, and the rectangle A B C D, will be divided into 42 
equal squares, the side of each being one chain. 



234 LAND-SURVEYING. (Part V. 

H G 



VT'r ■ \ 




XI 

X: 

...;....)■ 
1/ • 



) 



E F 

Next, by a scale of 4 chains to an inch, draw tlie line EF^ 
7 chains. At E and F erect the perpendiculars E H and F G, 
each of which make = 6 chains ; and join H G. Divide the 
lines E F and H G, each into 7 equal parts ; and the lines E H 
and F G each into 6 equal parts ; join the opposite points of 
division, and the rectangle E F G H will be divided into 42 
equal squares, the sides of which will be exactly half the size 
of those in the rectangle A B C D. - 

Then, with your pencil, draw within the rectangle E F G H 
the fences contained within the rectangle A B C D ; making 
each fence pass through its proper situation in the corresponding 
squares, which may be done by observing where the lines 
forming the squares, intersect the fences. Afterward trace the 
fences with Indian ink, as before directed. 

Note. — In copying or reducing a large plan, by this method, you ought 
to number the corresponding squares, in the circumscribing rectangles, with 
the same figures, in order to prevent mistakes. These figures, as well as 
the lines forming the squares, should be made with a pencil, and effaced 
after the plan is copied. 



METHOD V. 

By the Pentagraph. 

No instrument that has hitherto been invented is equal to 
the pentagraph, for reducing, copying, or enlarging plans. It 



Part V.) LAND-SURVEYING. 235 

is not only the most expeditious, but also the most correct ; as 
it copies every straight and curved line with the greatest ex- 
actness. It is as useful to an experienced draftsman, as to those 
who have had but little practice in drawing. It saves much 
time either in copying, reducing, or enlarging plans ; and may 
be used with equal facility for copying figures, profiles, sea- 
charts, maps, landscapes, &c. &c. 

Pentagraphs may be had of most of the Mathematical Instru- 
ment Makers ; and in Mr. Jones's Catalogue, the price is from 
1/. 18s. to 61. 16s. 6d. 



DESCRIPTION OF THE PENTAGRAPH. 

See Plate V. 

The pentagraph is generally made of wood, or brass, from 12 
inches to two feet in length, and consists of four flat bars or 
rulers ; two of them long, and two short. The two longer are 
joined at the end A, by a double pivot, which is fixed to one 
of the rulers ; and works in two small holes placed at the end 
of the other. Under the joint is an ivory castor, to support 
this end of the instrument. The two smaller rulers are fixed 
by pivots at E and H, near the middle of the larger rulers ; 
and are also joined together at their other end, G. 

By the construction of this instrument, the four rulers always 
form a parallelogram. There is a sliding box on the longer 
arm, and another on the shorter arm. These boxes may be fixed 
at any part of the rulers, by means of their milled screws ; and 
each of these boxes are furnished with a cylindric tube, to carry 
either the tracing point, pencil, or fulcrum. 

The fulcrum, or support K, is a leaden weight ; on this the 
whole instrument moves when in use. 

To the longer instruments are sometimes placed two move- 
able rollers, to support the pentagraph, and facilitate its motions. 
Their situation may be varied as occasion requires. 

The graduations are placed on two of the rulers, B and D, 
with the proportions of \, \, J, &c. to T ' 2 , marked on them. 



236 LAND-SURVEYING. (Part V. 

The pencil-holder, tracer, and fulcrum, must in all cases be 
in a right line, so that when they are set to any number, if a 
string be stretched over them, and they do not coincide with 
it, there is an error either in the setting or gradations. 

The long tube which carries the pencil, or crayon, moves 
easily up or down in another tube ; there is a string affixed to 
the long, or inner tube, passing afterwards through the holes 
in the three small knobs to the tracing point, where it may, if 
necessary, be fastened. By pulling this string, the pencil is 
lifted up occasionally, and thus prevented from making false or 
improper marks upon the copy. 



THE USE OF THE PENTAGRAPH. 

To reduce a Plan in any of the Proportions \, i, \, J, fyc. as 
marked on the two Bars B and D. Suppose for example, \ 



Place the two sockets, at §, on the bars B and D, the ful- 
crum, or lead weight at B,.the pencil socket with the pencil, 
at D, and the tracing point at C. Fasten down upon a smooth 
board, or table, a sheet of white paper under the pencil D, and 
the original map, &c. under the tracing point C, allowing your- 
self room enough for the various openings of the instrument. 
Then with a steady hand carefully move the tracing point C, 
over all the lines on the map ; and the pencil at D will describe 
exactly the same figure as the original, but \ the size. In the 
same manner for any other proportion, by setting the two 
sockets to the number of the required proportion. 

The pencil-holder moves easily in the socket, to give way to 
any irregularity in the paper. There is a cup at the top for 
receiving an additional weight, either to keep down the pencil 
to the paper, or to increase the strength of its mark. 

A silken string is fastened to the pencil-holder, in order that 
the pencil may be drawn up off the paper, to prevent false 
marks when crossing the original plan, in the operation. 




^M; 



Part V.) LAND-SURVEYING. 237 

If the original should be so large, that the instrument will 
not extend over it at one operation, two or three points must 
be marked on the original, to correspond with the same upon 
the copy. The fulcrum and copy may then be removed into 
such situations as to admit the copying of the remaining part 
of the original ; first observing, that when the tracing point 
is applied to the three points marked on the original, the 
pencil falls on the three corresponding points upon the copy. 
In this manner, by repeated shiftings, a pentagraph may be 
made to copy an original of ever so large dimensions. 



To enlarge a Plan in any of the proportions, \,\, i, Sfc. 
Suppose h. 

Set the two sockets at |, as before, and change places of the 
pencil and tracing point ; namely, place the tracing point at D, 
and the pencil at C 



To copy a Plan the same size as the Original. 

Place the two sockets at J, the fulcrum at D, and the pencil 
at B. In this case, the lines upon the new plan will be re- 
versed, in copying. 

Note 1. — There are sometimes divisions of 100 unequal parts laid down 
on the bars B and D, to give any intex-mediate proportion, not shewn by the 
fractional numbers. 

2. — Pentagraphs of a greater length than two feet are best made of hard 
wood, mounted in brass, with steel centres, upon the truth of which depends 
entirely the equable action of this useful instrument. 

3. — Though I have given various methods of reducing plans, I would ad- 
vise the learner, after he has found the contents from a plan of 2 chains, or 
of 1 chain to an inch, to draw another rough plan, of the same size which he 
intends his finished one to be ; and then to transfer it to a clean sheet by any 
of the foregoing methods. This may appear a little tedious, but it will make 
the learner very expert in laying down his lines, which will be found of great 
advantage to him, when he enters upon the practical part of surveying. 



238 LAND-SURVEYING. (Part V. 



TO EMBELLISH A PLAN. 

In order to make a neat, finished plan, some knowledge of 
drawing is absolutely necessary. The learner should also be a 
proficient in plain and ornamental penmanship ; or he will not 
be able to finish a plan, either with beauty or elegance. Every 
person who would excel in this art, should devote all his leisure 
hours to copying and making out drawings, either from plans 
or copperplates well executed ; as nothing but practice will 
make a good draftsman. 



METHOD I. 

Plans neatly finished with Indian Ink and Colours. 

Having transferred the plan to a clean sheet of drawing-paper, 
or to a skin of parchment or vellum, by any of the foregoing 
methods, draw ail the straight lines very finely, by the edge of 
a ruler, with a drawing-pen and Indian ink ; but the curved 
lines must be drawn by a steady hand. 

Proceed next to make the representation of hedges, bushes, 
trees, woods, gates, stiles, bridges, the bases of buildings, &c. &c. 
in their proper places ; running a single dotted line, in an open 
field, for a foot-path, and a double one for a carriage -road. 

Hills may be shaded with a brush or hair-pencil and Indian 
ink. The first wash should be weak, and the edges of the shade, 
particularly at the top and bottom of a hill, must be softened 
off with clear water, and a clean brush, kept for that purpose, 
at one end of the pencil-handle ; the other end being occupied 
by the Indian ink brush. 

When the hills are very steep, and rise one above another, as 
those in Wales, Derbyshire, Yorkshire, Westmoreland, Cum- 
berland, Northumberland, and Scotland, they must all be shaded 
according to their various inclinations ; always letting one wash 
dry before another is laid on ; and never neglecting to soften 
off the edges of each shade with Avater. 



Part V.) land-surveying. 239 

If some parts of the hills be rocky, tint them with a colour 
resembling stone, after they have been shaded with Indian ink 
and a hair-pencil, in the manner exhibited in No. 2, Plate VII. 

It may also be observed that when the inclination of a hill 
is considerable, it is never noticed by Surveyors, in shadino- 
or finishing their plans ; and if hills be flat at the top, they 
are left nearly white. 

The method of shading high moorish ground, and hilly fields, 
may be seen in Plates VI. and VII. ; except they must not be 
done with lines, in imitation of engraving, but with repeated 
washes of Indian ink. 

After hills have been properly shaded with Indian ink, they 
may then be coloured in the manner hereafter directed for 
meadow, pasture, and arable land. 

Lakes, rivers, brooks, &c. may also be shaded with a brush 
and Indian ink, pretty strongly at the edges, and softened off 
towards the middle ; and when they are dry, they may be 
washed over with a light tint of Prussian blue. The shape of 
arrows should also be made in brooks and rivers, to shew in 
what direction the streams run. 

Meadow and pasture ground should be coloured with a trans- 
parent green, the pasture rather lighter than the meadow ; arable 
land with various shades of fine brown, so that too many fields 
may not appear exactly alike ; and some Surveyors use both 
red, blue, lake, and yellow, in colouring plans. 

If the quick-Avood hedges be not made with a pen and Indian 
ink, in imitation of bushes, they may be represented by run- 
ning narrow shades of colouring along the black lines w T hich 
form the boundaries of the different inclosures. 

Roads should be washed with a brownish tint, and the bases 
of buildings with a red one, or with Indian ink, laid on with a 
brush of a convenient size ; as it is difficult to manage large 
brushes in shading small spaces. 

Sands upon the sea-shore, may be washed over with a mixture 
of brown, lake, and gamboge. 

Greens of various shades may be composed of blue and yellow ; 
a pleasing variety of brownish tints may be produced by mixing 



240 LAND-SURVEYING. (Part V. 

lake, red. or yellow, with a little brown ; and a shade for water 
may be formed of Indian ink and Prussian blue. 

All the washes should be made thin, and laid on in a very 
neat manner ; as nothing disfigures a plan or a map so much as 
daubing on the colours too thickly. 

If the estate be small, the area of each inclosure may be put 
down in some vacant part of the plan ; but if it be large, the 
areas must either be entered within the fields themselves, or in 
a book of particulars, which may also contain any remarks that 
the Surveyor may think necessary to make to his employer, 
concerning the estate. 

In some convenient part of the plan, write, in various hands, 
with Indian ink, the title of the estate, ornamented with a com- 
partment or device. In another vacancy, introduce the scale 
by which the plan has been laid down ; and also a meridian- 
line, with the compass or flower-de-luce pointing to the 
north. 

The whole may then be bordered with black lines, at a con- 
venient distance from each other ; and the space between them 
shaded with a hair-pencil and Indian ink. See Plates IX. and 
XI. (Also y vide Xotes 3. ±. 5, an d G, page 378. ) 

Note 1. — If the learner examine a well -finished, coloured map of England, 
or any other country, he will fully comprehend what has been said on the 
subject of embellishing plans. 

2. — Indian ink must always be used in planning ; and as it is frequently 
of a very bad quality, it is advisable to try it before you purchase, by wetting 
one end of the cake, and rubbing it upon white paper. The blackest and 
freest is considered the best. 

3. — The most convenient colours are those ready prepared in cakes, which 
must be used in the following manner : Dip one end of the cake in dear 
water, and rub a little of it upon a clean wedgewood or earthen plate ; then 
mix it with water, by your hair-pencil, until you have brought it to any con- 
sistency you please. Indian ink must be prepared for use in the same way. 

4. — Mr. James Newmans water-colours, No. 24, Soho-Square, London, 
are considered the best. The following will be found quite sufficient for Land- 
Survey ors ; viz. 



Part V.) LAND-SURVEYING. 241 

Vandyke Brown. Yellow Ochre. Vermillion. 

Raw Sienna. Indian Yellow. Prussian Blue. 

Burnt Sienna. Light Red. Prussian Green. 

Gamboge. Lake. Sap Green. 

By means of these colours, a great variety of tints may be formed ; and a 
little practice will soon enable the learner to produce any shade that may 
be wanted for plans, or maps. 

5. — When the price for measuring and planning is very small, Surveyors 
generally finish their plans neatly ; but without either colours, compart- 
ments, or embellishments of any kind. 

6. — Professional Surveyors always enter in their Field-Books, the day of 
the month and date of the year, when they begin to survey an estate ; and 
in finishing their Plans, they date them accordingly, and also insert their 
own names, in order that gentlemen may know when, and by whom their 
estates were surveyed. 



METHOD II. 

Plans highly finished with Indian Ink and Colours. 

The foregoing method of finishing plans, is very expeditious, 
and may suffice when the price allowed for surveying will not 
admit of much time being spent in making embellishments ; 
but when a highly finished plan is wanted, the following method 
must be adopted. 

Meadows. 

With a pen, or a very fine pointed hair-pencil, and light 
Indian ink, make perpendicular and inclining strokes over the 
whole meadow, as represented in No. 1, Plate VI. ; and then 
wash it with a fine, transparent green. The strokes must be 
of various lengths; but none of them should exceed the 10th 
part of an inch. 

Pasture Grounds. 

Pastures may be shaded with upright and sloping strokes, of 
various lengths, as represented in No. 2, Plate VI. ; and then 

R 



242 LAND-SURVEYING. (Pari V. 

w i- ar with a green, somewhat inclining to yellow. 

H one of the strokes shonld ex _ \ art of an inch in 

lencrth. 



By the edge of a ruler, or by the hand, draw (in short da- 
fine parallel lines, at equal distances from each other, so aa 
_ the fields the appearance of being divided into ridges and 
farrows, as represented in Nos. 3 and 4, Plate VX ; and then 
wash each field over with a different tint of brown, inclining - 
yellow. 

n=£dds :.-: ..:. ; ::>.. : ] hi this ma:: a plan a 

fine appearance. 

3f :■:■/'$. 

With a pen. or a hair-pencil, draw the representation of a 
few k :■.::;:■- Dc is, if there be any on the moor. 

Draw also here and there, small bushes, ta represent heath, 
broom, whins, and such like brushwood" as usually grow upon 
moors. 

Make likewise tofts of grass, if :he moor is pasturable; and 
:: fill up all the vacant spaces with perpendicular and in- 
clining strokes, as rej resented in Nos. 1 and 2. Plate VI 

If them: >i be high, hilly, and rugged, with pools of water, 
caverns, roads, &c. it must be shaded with lines, in imitation of 
engraving, is exhibited in X:. 5, Plate VX; if any parts be 
wet and marshy, they must be done in the same manner as 
marshy ground ; and if the moor contains large stones, re : 
or trees, they must not be omit: 

When vou have finished shading with Indian ink. you must 
then colour the different parts of the moor, in the same manner 
i- fchey appear in nature. The parts producing herbage, nrast 
be washed with a greenish colour, inclining to blue ; the dark 
parts with a brownish: tint ; the lighter parts with a yellowish 
on^. : and the shrubs and bushes maybe touched up 

th a fine, lightish green. 
I: the moor contains whins, first wash them with green : and 



Plate YJ . 




If////* Ufr//s// (wittid. 




Part V.) LAND-SURVEYING. 243 

then touch them up on the west side Math yellow, which will 
give them the appearance of being in blossom. 

By proceeding as above directed, a variety of pleasing effects 
and shades will be produced : and you will be able to give 
your plan a very fine appearance, and make it resemble even 
nature itself. 

Marshy Ground. 

With a pen, or a fine pointed hair-pencil, and palish Indian 
ink, draw, by the hand, shortish horizontal strokes of various 
lengths, pretty closely to each other. Make also the representa- 
tion of reeds, rushes, sedges, and strong herbage, as exhibited 
in No. 1, Plate VII. ; wash the whole over with a palish green, 
inclining to blue; and then touch up the reeds, rushes, 
sedges, &c. with a stronger green, which soften off either towards 
the right or left, with a lighter one, or with clear water. (See 
the method of shading trees.) 

Sands and Rocks. 

Sands upon the sea-shore, &c. must be represented by small 
dots, with a pen and Indian ink; loose stones by figures re- 
sembling small circles and ovals, but more irregular ; and rocks 
must be made to appear rugged and rough, and to rise in suc- 
cession, one above another, as exhibited in No. 2, Plate VII. 
The sands may then be washed over with a mixture of brown, 
lake, and gamboge ; and the stones and rocks coloured with 
such tints as will give them the appearance of nature. Some 
stones and rocks are whitish, some yellowish, some greyish, 
others brownish, &c. ; hence the propriety of always taking 
their real colour into consideration, when we intend to give a 
faithful representation upon a plan. 

Trees. 
Trees always adorn and beautify the face of nature ; and 
when they are neatly drawn, with a fine pen and Indian ink, 
they give a plan a very beautiful and pleasing appearance. 

They must be made with vertical stems, neat, broadish tops, 
r2 



244 land-surveying. (Part V. 

shaded darker cm one side than the other; and black, horizontal 
shades at the bottom, as represented in No. 3, Plate VII. 

The lighter parts of the trees represent that side upon which 
the light is supposed to fall ; and the horizontal shades at the 
bottom are intended to denote the shadows of the trees, upon 
the ground. These shadows must always be made on the 
darker sides of trees ; and also of every other object, where 
shadows are intended to be represented. 

It is not material which side of a tree be left light ; but we 
must take care to make all the trees in the same wood, light on 
the same side ; for we cannot suppose that the light can fall 
on the right of some trees, and on the left of others, at the 
same time. 

When a sufficient number of trees have been made to give 
the wood an agreeable appearance, the vacant spaces must be 
filled up with small hushes, to represent the underwood. The 
whole wood should then be washed over with a lightish green ; 
after which, the tops of the largest trees may be touched up 
with a darker green, and with a little brown or yellow, in 
order to produce that pleasing variety _of tints which we so 
often behold and admire in nature. 

Note 1. — When the Indian ink, composing the trees, is not perfectly dry, 
it will run in washing the wood with green ; in order to avoid this, the 
green wash may be laid on before the trees and bushes are made. — This 
observation also points out the propriety of colouring fields, before the 
quickwood fences, are made with Indian ink. 

2. — The tops of trees are formed in various ways. Sometimes they are 
made with jagged edges, and filled up in the middle with irregular strokes, 
in different directions ; and some Surveyors form them entirely by hori- 
zontal lines of various lengths. 

3. — When trees are small, and neatly made, it is unnecessary to touch 
them up with any colour. 

4. — Quickwood hedges must be made with a pen and Indian ink, in imita- 
tion of bushes ; and when trees are properly introduced, they have a very 
good effect in the hedge-rows. (See Plates IX. and XI.) 



Lakes, Rivers, and the Sea-Shore. 
Water must first be coloured with a fine tint of Prussian blue ; 



Part V.) LAND-SURVEYING. 245 

and then shaded, by a pen, and Indian ink, with crooked or 
waved lines, bold near the edges, and fainter towards the 
middle, as exhibited in No. 4, Plate VII., which is intended to 
represent a mere or lake. 

Rivers and brooks must also be shaded with waved lines, 
continued from one end to the other, as represented in Plate 
XI. ; and the sea-shore in a similar manner, but much stronger 
and bolder than either lakes or rivers. 

N t e l . — Some draftsmen do not wash with Prussian blue, until they have 
finished shading with Indian ink ; but it is much better to colour the water 
before it is shaded, as the ink frequently runs when a wash is laid upon it. 

2. — Here it may not be improper to observe,, that in colouring lakes, rivers, 
&c. with Prussian blue, the wash should be pretty strong at the edges, and 
softened off with water, towards the middle. 



Hilly Ground. 

Meadow and pasture ground should first be washed w r ith a 
fine green, and ploughed land with a yellowish brown, as before 
directed ; the hills must then be shaded in lines, with a pen 
and Indian ink, as represented in Nos. 5 and 6, Plate VII. 

The sides of hills may be shaded in the manner represented 
in the lower part of No. G ; and when the top of a hill is level, 
it must be left almost without shade. 

The greater the altitude of a hill, the deeper must be the 
shade ; but the level part of a valley between two hills, must 
be very faintly shaded. 

It will add greatly to the beauty of the plan or map, if all 
the hills be introduced in their proper places. When this is the 
case, and the hills are properly shaded, they form what is called 
a bird's eye mew ; it being supposed that the eye of the observer 
is elevated to some distance from the ground. 

What has been said on this subject will be fully comprehended 
by the learner, if he carefully examine the Plate to which I 
have already referred ; and also No. 5, Plate VI., which repre- 
sents a high, moorish district, shaded in a very neat and ex- 
pressive manner. 

b3 



246 LAND-SURVEYING. (Part V. 



Pleasure Grounds. 

In order to draw a true plan of pleasure-grounds, it is ne- 
cessary to measure such lines, in taking the survey, as will 
enable you to lay down correctly, the shrubberies, grass-plots, 
and fish-ponds ; the bases of summer-houses and alcoves ; and 
the turnings and windings of all the gravel- walks, &c. &c. 

The trees, bushes, bases of buildings, &c. &c. must then be 
neatly made ; the fish-ponds and grass-plots properly coloured 
and shaded, as before directed, for lakes and meadows ; 
and the gravel-walks washed with a fine brown inclining to 
yellow. 

Note 1. — If the mansion-house, stables, gardens, &c. &c. be situated within 
the pleasure-grounds, the greatest care should be taken to lay them down cor- 
rectly ; as a gentleman will easily discover the smallest inaccuracy in a plan 
of those places with which he is so well acquainted. 

2. — When pleasure-grounds are surveyed and planned with adjoining 
estates, the same scale must, of course, be used for the whole ; but when the 
former are measured separately, a large scale should be chosen, in order to 
allow sufficient room to plan every object distinctly.. 



Gardens. 

Gardens should be correctly and neatly planned ; and finished 
in a tasteful and elegant manner. 

The hot-houses, green-houses, grass-plots, gravel-walks, beds, 
&c. &c. should all be drawn and laid out, as they appear in the 
garden itself. 

The divisions between the different beds may be made with 
short dashes, as represented in Nos. 3 and 4, Plate VL ; the 
beds should then be lightly shaded with a pen and Indian ink ; 
rows of bushes inserted along the sides of the walks, and at the 
divisions of the various beds ; and here and there a few scat- 
tered trees should be made, as before directed, if there be any 
in the garden. 



Part V.) LAND-SURVEYING. 247 

The gravel-walks must then be washed with a yellowish 
brown ; the grass-plots with green ; and the different beds with 
a light tint of yellow, red, lake, blue, green, or any other colours, 
so as to produce a pleasing variety ; and the trees may be 
touched up with a little dark green ; and occasionally a brownish 
or yellowish tint may be used, and give them an autumnal ap- 
pearance. 

Note. — When plans are to be finished with colours, it is not necessary to 
shade them so much with Indian ink, as when they are finished with Indian 
ink only. 



The Bases of Buildings. 

The outlines of the bases of buildings must be made with a 
drawing-pen and Indian ink, bold and black on the south and 
east sides, or on the north and west sides ; and the spaces in the 
middle filled up with oblique lines, as represented in No. 7, 
Plate VII., which is given expressly for the purpose of making 
the learner fully acquainted with the method of shading the 
bases of buildings, drawing the plans of villages, towns, &c. &c. 

Note 1. — When a proprietor wishes to have a plan of his buildings, offices, 
yards, &c. &c. upon a large scale, the dimensions should be taken in feet and 
inches, or in feet and tenths, which is preferable ; because the chains and 
tenths of a chain, upon the plotting-scale, may then be considered as feet and 
tenths, and used accordingly in planning ; or when it is more convenient, each 
chain may be called ten feet ; consequently, each division will then become 
one foot. (See Note 3, Prob. I. Part III.) 

2. — When it is intended to lay down buildings by a large scale, the thick- 
ness of the walls, the lengths and breadths of rooms and passages, the widths 
of doors and windows, the projections of fire-places, and other necessary 
dimensions, should be taken, in order to produce a correct plan. 

3. — After the base of a wall has been formed by parallel lines, drawn at 
such a distance from each other as to exhibit the wall's thickness, the space 
between these lines may then be shaded by oblique lines as before directed. 
The door- ways should be left open ; the window-bottoms represented by omit- 
tingto shade them with oblique lines ; the chimney bottoms or fire-places ex- 
hibited by making the inside of the wall to project into the room, at right- 

R 4 



248 laxd-suhveyixg. (Part V. 

angles ; and the steps of the stairs denoted by parallel lines, drawn at proper 
distances from each other. The insides of the rooms may either be left white 
or coloured, at the option of the draftsmen ; and if it be thought tedious to 
ehade the bases of the waDs with oblique lines, they maybe done with a brush 
and Indian ink. 



4. — The name of every room, office, yard, Jce. must be given, either within 
the rooms themselves, or in the margin of the plan ; and when the premises 
are extensive, the names of the rooms, out-offices, yard?, kc. will be numerous ; 
there will probably be the kitchen, back-kitchen,parlour, hall, breakfast -room, 
dining-room, drawing-room, dairy, pantry, stairs, brew-house, wash-house, 
coal-house, carriage-house, stables, cow-house, calf -house, hog-stye, soil-hole, 
barn, stable-yard, court -yard, orchard, garden, &c. &c. What has been said 
on this subject will be easily comprehended by inspecting No. 2, Plate V. ; 
which is the ground plan of a small house, laid down by a large scale, in order 
to show the learner how he must proceed with plans of a similar nature. 

5. — "Whehpreniises are to be sold, every convenience should be pointed out, 
on the plan, in order to promote the sale ; and it wiil be found very advan- 
tageous to have plans of the cellars and the upper stories, and even the ele- 
vations ; but this is more properly the business of an Architect than that of a 
Land- Surveyor. Some persons, however, will find it of considerable advan- 
tage to obtain a knowledge of both these sciences ; as gentlemen frequently 
want not only plans of their estates, but also architectural draughts of their 
buildings. 



The Elevation s >f Buildings. 

In order to give & perspective view of the elevation of a build- 
ing, it is necessary to be acquainted with the art of drawing in 
perspective; but an architectural view may be produced by 
taking the dimensions of the building, and laying them down 
by a scale of equal parrs. 

"When it is intended to give the elevation of any buildings 
belon-dno- to a farm, or the elevation of a mansion-house and 
offices belonging to a gentleman's estate, the length from end 
to end. the perpendicular height from the ground to the 
. the height of the gable-ends, the height and breadth of the 
chimnev-tops, the height and width of the doors and windows, 
their situations in the walls, and every other necessary dimen- 



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Part V.) LAND-SURVEYING. 249 

sion must be measured ; then these dimensions being correctly 
laid down by a scale, will give an architectural view of the 
elevation of the building in question. 

AVhat has been advanced on this subject will be further illus- 
trated by referring to No. 8, Plate VII. , which is an architectural 
view of a gentleman's house, given for the inspection and im- 
provement of the learner. The house itself is built with gable- 
ends, but the roofs of both the wings are hipped at one end, 
which make a pleasing contrast in the elevation. 

Note 1. — After the outlines of an elevation are drawn, the common method 
of shading is by a brush and Indian ink ; as it is generally thought too 
tedious to shade with strokes, in imitation of engraving. The roof should 
be shaded pretty strongly at the ridge, and softened off towards the middle, 
with water. It may then be washed with Prussian blue ; and if the washes, 
both of Indian ink and colour, be light and often repeated, a more agreeable 
softness will be produced than by laying on only two or three strong washes. 
When the roof has been thus shaded, lines may be drawn parallel to the eaves, 
decreasing gradually in their distance from each other towards the ridge, to 
represent the edges of the slates. If the house be covered with tiles, the 
lines must be at equal distances from each other ; because tiles of different 
sizes are never laid upon the same house. 

2. — If the front of a building project beyond the wings, it must be denoted 
by making its shadow fall upon one of the wings ; but if the wings project 
beyond the front, the shade of one of them must be made to fall upon the 
front. (See No. 8, Plate VII., where the shade of the front falls upon the 
right wing ; if the wings had projected, the shade of the left wing would 
have fallen upon the front.) 

3. — If a house be built of brick, it may be coloured red ; if of stone, a 
colour may be chosen to resemble it ; and when a roof is covered with grey 
slates, blue slates, or red tiles, it may be coloured accordingly. Sometimes 
the front of a building is shaded with Indian ink, the roof tinted with blue, 
and the stone door-posts, window-jambs, string-courses,chimney-tops,&c.&c. 
coloured so as to resemble stone. Indian ink, however, is generally used for 
fronts, in preference to any colour ; as it is considered to give buildings a 
much richer appearance. 

4. — If there be trees about the buildings, they may be etched with a pen 
and Indian ink, in imitation of engraving ; the ground in front should be 
properly shaded ; the gravel-walks coloured with a light brown ; and if the 
elevation be bordered with black lines, as in No. 8, Plate VII., the sky may 
be coloured with a fine blue, or shaded with Indian ink. 



250 land-surveying. (Part V. 

5. — The elevations of buildings belonging to estates that have been sur- 
veyed, should be given on vacant parts of the plan, as embellishments ; it is 
very seldom indeed that they are drawn in their true situations, because they 
would intercept the view of the ground plot ; and besides, they are generally 
laid down by a much larger scale. The mansion-house of a nobleman, well 
executed, on a vacant part of the plan of his estate, has a very pleasing effect ; 
and will never fail to gratify the proprietor. 

6. — It is almost superfluous to remind the young draftsman that he should 
always keep his hands perfectly clean, and also cover his plans and maps with 
clean paper, (particularly under his hands,) to preserve them from being in 
tho least soiled in drawing them ; as nothing exhibits the carelessness of a 
draftsman in a more conspicuous light, than seeing his work besmeared with 
dust, ink, or colours. 

METHOD III. 

Plans highly finished with Indian ink. 

A plan highly finished with Indian ink only, has a very- 
elegant appearance, and is considered, by most persons, to ex- 
cel those done in colours ; hut the process is very tedious, and 
requires much time to do it neatly ; however, if the Surveyor 
be well paid for his time, he ought to finish his plans in that 
manner which is most likely to give satisfaction to his em- 
ployers. 

Many Surveyors keep plans by them, finished in various 
ways, as specimens, in order that gentlemen may have an op- 
portunity of choosing in what manner they will have the plans 
of their estates executed. 

Shading with the Pen. 

In finishing a plan with Indian ink, a fine pen ought to be 
used ; and the fields should be shaded in a great variety of 
forms, in imitation of engraving, as exhibited in Plate V. IX. 
and XI. 

Some fields should be done lighter, and others darker, so as 
to produce a pleasing contrast of light and shade. Some may 
be executed in such a manner as to resemble corn-fields, as in 
Nos. 1 and 6, Plate IX. ; and 13 and 16, Plate XI. ; and others 
may be shaded like meadow and pasture, as exhibited in Nos. 
1 and 2, Plate VI. 



Part V.) LAND-SURVEYING. 251 

High, moorish ground should be shaded as represented in 
No. 5, Plate VI. ; and marshy grounds, sands, loose stones, 
rocks, trees, water, hilly fields, and the bases of buildings, as 
denoted in Plate VII. ; and even the elevations of buildings 
look very elegant, when they are finely shaded with lines, as 
No. 8, in the Plate to which we last referred. 

Note. — In finishing a plan with Indian ink only, it is necessary to shade it 
much closer and deeper, than in finishing with Indian ink and colours. 



In making finished plans, no ornaments or embellishments 
will compensate for bad penmanship. 

Writing, German-text, Printing, and Figures, are all essen- 
tially necessary for a draftsman; and whoever would excel in 
the art of planning, should use his utmost endeavours to be- 
come a complete and elegant penman. 

He should practise the various hands, either by copies well 
written, or by good copper-plates, until he can make all the 
letters and figures correctly, and with true taste ; and it will save 
him much trouble in making compartments and devices, if he 
can acquire the art of flourishing and ornamenting neatly and 
elegantly with the pen. (See Notes 3, 4, 5, and 6, page 378.J 

Ornaments. 

Any compartment or device may be chosen to fill up the 
vacant corners of a plan, such as the compass, scrolls of paper, 
wreaths or festoons of leaves and flowers, branches or sprigs of 
oak, palm-tree, weeping-willow, myrtle, laurel, olive, &c. &c. 
Also shields, coats of arms, columns supporting vases or urns, 
mathematical instruments, cattle, sheep, or whatever else may 
please the fancy of the draftsman. 

Ornaments on Plate IX. 

In the N. W. corner is a device formed of an oak branch, 
leaves, and acorns on the left side ; and on the right side is a 



252 LAND-SURVEYING. (Part V. 

branch of large pointed leaves resembling sedges or sweet flags, 
intertwined with a string of small leaves; and both branches 
are united at the bottom by a bunch of riband. 

In the S. W. corner is a scroll of paper, supported by a 
fluted column ; by the side of which are some ears of corn, and 
at the bottom a few blades of grass and herbage. 

In the N. E. corner is the sun in his meridian splendour, 
with a fancy device resembling an ogee cornice, fronted with 
reeds ; and from each end of the cornice is suspended a festoon 
of small leaves. 

In the S. E. corner is a plotting-scale ; a pair of compasses, 
two drawing-pens, and a writing-pen, interwoven with a gar- 
land of small leaves and berries, resembling those of the 
myrtle. 

Ornaments on Plate XL 

In the N. W. corner is a fancy device, in the form of an 
oval ; and in the N. E. corner is a rectangular device, with the 
exception of the arch at the top. This device is ornamented 
with a bunch of riband, and two festoons of small leaves and 
berries, hanging upon two scutcheons, or shields. 

In the S. W. corner is a column, at the top of which is a 
vase encircled with leaves and flowers. On the west of the 
column, Britannia is seated, leaning on her shield, holding a 
spear in her right-hand, and with her left-hand pointing out 
the science of Surveying. To the east of the column are two 
sheep, emblems of agriculture. 

The plotting-scale, drawing-pens, &c. are nearly similar to 
those in the last plate. 

In the S. E. corner is a parallel ruler, a plane table, a terres- 
trial globe, a crowing cock, and a youth seated upon a bee-hive, 
with a pair of compasses in his hand, at work upon plate XII. 

The cock is an emblem of early rising, and the bee -hive may 
be considered as an emblem of industry ; and it may here be re- 
marked that it is impossible to attain eminence in the art of 
Surveying, without early rising, industry, and perseverance. 



Part V.) LAND-SURVEYING. 253 

MISCELLANEOUS INSTRUCTIONS 

RELATING TO 

SURVEYING, PLANNING, CASTING, VALUING, &c. &c. 



1. The title of a plan should set forth the name of the pro- 
prietor ; and also the name of the township, hamlet, parish, and 
county, in which the estate is situated. 

2. The names of the adjoining lordships, or the names of the 
proprietors of the adjoining lands, should be given on the plan, 
in order to point out clearly the situation of the estate, and cor- 
roberate the title. 

3. All principal roads passing through the estate, from one 
highway to another, should be laid down ; and the places to 
which they lead, specified. 

4. All foot-paths and bridle-roads should be pointed out, in 
order to determine the public right; and guard against en- 
croachments. 

5. All occupation and privileged roads, through adjoining 
estates, should be noticed either on the plan, or in the reference- 
book. 

6. All ancient highways leading through the estate, although 
not now in use, should be particularly specified, and the names 
of the proprietors given, to show in whom the privilege of re- 
opening them, if necessary, is vested. 

7. The ancient and proper names of fields should be pre- 
served ; as it generally creates confusion and mistakes, when 
new ones are assigned without sufficient authority. 

8. It has already been observed, that the extremities of the 
ditches are generally the boundaries between adjoining fields ; 
this, however, is not always the case, as the stem of the quick- 
wood sometimes forms the boundary; hence the necessity of 
obtaining an assistant who is well acquainted with all the local 
customs of the place. 

9. The greatest care must be taken to find the area of each 
field correctly ; and particularly if the survey be taken for an 
inclosure, or to make a valuation for the land-tax, poor-rates, 



254 LAND-SURVEYING. (Part V. 

county-rates, and other assessments ; for it is evident that if 
the surrey be incorrect, the valuation can never be equitable ; 
and will consequently produce nothing but disputes and dis- 
satisfaction among the proprietors and occupiers, instead of 
peace, harmony, and friendship. 

10. In valuing for an assessment, great care should be taken not 
to over-rate the land that is of a poor quality, and lies far from 
the means of improvement ; for bad land costs the occupier as 
much in labour and seed, as good land, and is far less produc- 
tive. (See more observations on valuing land, in Part VI.) 

11. In reducing a plan for portable use. care should be taken 
to choose a scale sufficiently large to exhibit all the irregularities 
in the fences, buildings, &c 

12. Several small farms, or detached pieces of land, belonging 
to one proprietor, may be laid down upon the same sheet. 
They ought not, however, to be joined together, but planned as 
separate estates. 

13. When one sheet of drawing-paper is too small to contain 
the survey, two or more must be neatly pasted together ; and 
when those parts that have been wet with the paste, are nearly 
dry, they may be made smooth by a warm iron. The edge of 
one of the sheets should be cut even, and laid nearly half an 
inch over the edge of the other sheet ; and a piece of clean 
paper should be laid under the iron, to prevent it from soiling 
the plan. 

1-i. It has already been observed that the surveying-chain 
should frequently be measured. The readiest method of doing 
this, is to drive two stakes or pins into the ground, exactly at 
the distance of 22 yards from each other. Professional Sur- 
vevors measure their chains in this manner every morning, 
when they are engaged in extensive measurements. When 
the chain has become too long, it is better to cut a little from 
several of the links, than to take off the rings ; care, however, 
must be taken to keep each 10 links of an equal length, or the 
dimensions will be incorrect. 

15. The book of particulars, before-mentioned, is generally 
called M A Terrier of the Survey," and should contain references 
corresponding to those upon the plan; also the name of each 



Part V.) LAND-SURVEYING. 255 

field, or the name of the proprietor, or of the occupier ; and 
the area of each field, in acres, roods, and perches. If the Sur- 
veyor value the estate, the Terrier ought to contain the value 
per acre to let, or for sale ; the annual value of each field to let, 
or the total value for sale ; and also the cultivation of each 
field : thus will the proprietor be furnished with every neces- 
sary particular relating to his estate. 

16. The Terrier may likewise contain remarks and obser- 
vations on the quality of the soil; and point out the method 
of improving wet marshy grounds, by draining them; com- 
mons and waste lands, by inclosing them ; large fields, by 
dividing them ; &c. &c. 

17. Some Surveyors return three measurements of each field 
in the Terrier ; viz. the land in cultivation ; the hedges and 
waste land ; and the total quantity, or sum of both. 

18. In giving the cultivation of each field, the permanent 
meadows, or those which the tenant is prohibited from breaking 
up, should be particularly noticed. 

19. In writing out a valuation-book for the purpose of making 
assessments, all the lands and tenements in the occupation of the 
same tenant, should be collected together ; and put down on 
the left -hand page of the book. At the top of the page must 
appear the name of the tenant ; and in the first and second 
columns respectively, the names of the proprietors and the num- 
bers on the plan. The third, fourth, fifth, and sixth columns, 
must contain the name, measurement, value per acre, and total 
value of each field respectively. The right-hand page may be 
left blank for incidental remarks, when a change of occupation 
takes place ; or when any circumstance occurs that affects the 
arrangement of the book. 

20. When the valuation is high, it is frequently thought pru- 
dent to calculate the assessments from one-fourth, one-half, or 
three-fourths of the amount ; this, however, is more properly 
the consideration of the occupiers, than that of the Land-Sur- 
veyor. Sometimes the assessments are calculated from one- 
half, or three-fourths of the valuation of the land ; and from 
one -fourth of the valuation of the buildings. 



256 land-surveying. (Part V. 

A TERRIER OF THE SURVEY IN PLATE IX. 



j 

© 

o 


Names 
of the 
Fields. 


Cultivation 

of the 

Ground. 


Area 

in 

A. R. P. 


Value 

per 

Acre 

to rent. 

£. s. d. 


Total 
Value 

per 

Annum 

to rent. 

£. s. d. 


1 


Calf Garth ... 


Pasture 


1 20 


2 12 6 


2 19 Of 


2 


Lane Close ... 


Arable 


2 2 38 


1 16 


4 18 6£ 


3 


Low Close 


Permanent ) 
Meadow J 


2 10 


2 2 6 


4 7 7} 


4 


Turnpike Close 


Arable 


13 1 28 


1 14 


22 16 5^ 


5 


Daisy Field . . . 


Meadow 


11 9 


1 15 6 


19 12 5{ 


6 


Triangle 


Pasture 


12 2 18 


2 3 6 


27 8 7£ 


Sura Total 




43 3 




82 2 91 









Note 1. — The annual value of each field may be found from the area, 
and the value per acre, by the Rule of Three' ; but when the calculations 
are numerous, much labour may be saved by using Hudson's Land Valuer's 
Assistant. 

2. — If one tenant occupy all the foregoing estate, his rent will be 82/. 
2«. 9±d. per annum ; and if the assessments be made from three-fourths of 
the annual value, he will be assessed at 62/. 12s. Id. 

3. The Terrier may be divided into any number of columns, to suit the 
purpose of the Surveyor ; and when the observations, remarks, Lc. are too 
numerous to be contained in the columns of one page, each two opposite pages 
may be divided into columns, in which may be entered every necessary infor- 
mation relating to the estate. 

4. — In extensive surveys and valuations, an alphabetical index should be 
annexed to the Terrier or Valuation-Book, in order that the name of any par- 
ticular proprietor or occupier may be more readily found. 





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]/,:C,,\/r\:r Close 2 „ 2,-3$ 

■ \/r\Vl>,.v/.e,W Close <2 „ () , f0 

I'lff S/ty//cers Close 13. / .. 26 

■ l//:l7/vr/,r//r Close. // » O .. '9 

Mi- .Ml,, r,li Close J2 .. 2 „ /S 

Total. IS. O ., 3 



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Wf- 8 tinker* Close 
\$r..U,(tAcr:r Close. 



.'2 „ 2 ., 38 

Q „ (> . 10 

.13 .. / .. 2S 

VI .. (> ,. & 



WtHMrrnfi Close 12 .. 2 „ 16 



Total... A3* O .. ,3 



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LAND-SURVEYING. 



Part tf>t Mixfy. 

Rules and Directions for laying out any given Quan- 
tity of Land* in any proposed Figure ; for parting from 
any Field or Figure any Quantity of Land required ; 
and for dividing a Piece of Land among sundry Claim- 
ants in the Proportion of their respective Claims, or a 
Common, fyc* of variable Value, among any Number of 
Proprietors, in the Proportion of their respective Interests. 
Also, the Method of reducing Statute Measure to Cus- 
tomary, and vice versa. 



SECTION I. 

RULES AND DIRECTIONS FOR LAYING OUT ANY GIVEN 
QUANTITY OF LAND, IN ANY PROPOSED FIGURE; AND 
FOR PARTING FROM ANY FIELD OR FIGURE, ANY QUAN- 
TITY OF LAND REQUIRED. 

When the land to be laid out, or parted off, is given in acres, 
roods, and perches, it must first be reduced into square links ; 
in which process the following Table will be found extremely 
useful. 

When it is required to part off from any field, or figure, any 
quantity of land, it is generally necessary, first, to measure the 
whole, if the dimensions be not given. 

s 



258 



LAND-SURVEYING. 



(Part VL 



A Table for reducing Acres, Roods, and Perches, into 
Square Links. 



Acres. 


Sq. Links. 


[Perches. 


Sq. Lks. 


Perches. 


Sq. Lks. 


1 


100000 


1 


625 


1 21 


13125 


2 


200000 


2 


1250 


22 


13750 


3 


300000 


3 


1875 


23 


14375 


4 


400000 


4 


2500 


24 


15000 


5 


500000 


5 


3125 


25 


15625 


6 


600000 


6 


3750 


26 


16250 


7 


700000 


7 


4375 


27 


16875 


8 


800000 


8 


5000 


28 


17500 


9 


900000 


9 


5625 


29 


18125 


10 


1000000 


10 


6250 


30 


18750 


20 


2000000 


11 


6875 


31 


19375 


30 


3000000 


12 


7500 


32 


20000 


40 


4000000 


13 


8125 


33 


20625 


50 


5000000 


14 


8750 


34 


21250 


GO 


6000000 


15 


9375 j 


35 


21875 


70 


7000000 


16 


10000 i 


36 


22500 


80 


8000000 


17 


10625 


37 


23125 


90 


9000000 


18 


11250 


38 


23750 


100 


10000000 


19 
20 


11875 
12500 


39 


24375 


Roods 


Sq. Links. 
~ 25000 










2 


50000 










3 


75000 




1 







PROBLEM I. 

To reduce any number of Acres, Roods, and Perches, into 
Square Links. 

Rule. — Rednce the given quantity of land into perches, 
which multiply by 625, the number of square links in one 
perch, and the product will be the square links required. Or, 
find the equivalents of the acres, roods, and perches respectively, 
in the foregoing Table. 



Section I.) land-surveying. 259 



EXAMPLES. 

1 . Reduce 6 acres, 3 roods, and 25 perches, into square links. 

By the Rule. By the Table. 

a. R. P. sq. links. 

6 3 25 6 a. = 600000 

4 3 r. =. 75000 



27 



25 p. =£= 15625 



40 690625 Ans. 



1105 
625 



5525 
2210 

6630 
690625 Ans. 



2. Required the number of square links in 96 acres, 2 roods, 
and 36 perches. Ans. 9672500. 



PROBLEM II. 

To lay out, in a Square, any Quantity of Land proposed. 

Rule. — Extract the square root of the proposed area, and it 
will be the side of the square required. 

examples. 

1. Lay out, in a square, 7 acres, 1 rood, and 24 perches. 

sq. links. 
7 a. = 700000 
1 r. = 25000 
24 p. = 15000 

740000(860.2 links, the side of the square, 
64 

166)1000 
996 



17202)40000 
34404 



•5596 

s2 



260 



LAND-SURVEYING. 
D C 



(Part VI. 




In laying out the square, in the field, let A B represent one 
of its sides, which make = 860.2 links. At A, erect the per- 
pendicular A D, which make = AB; and at B, erect the per- 
pendicular B C, which make also = AB. Then measure the 
line C D, and if you find it = 860.2 links, the work is right. 

2. Required the side of a square, which shall contain 15 
acres, 2 roods, and 32 perches. Ans. 1253 links. 

PROBLEM III7 

Upon a given Line, to make a Rectangle that shall contain any 
proposed Quantity of Land. 

Rule. — Divide the proposed area by the given side, and the 
quotient will be the other side of the rectangle. 



EXAMPLES. 

1. Lay out 3a. 3r. 26p. in the form of a rectangle, one side 

©f which must be 850 links. 

sq. links. 
3a. = 300000 
3r. = 75000 
26p. = 16250 

85,0)391250(460.3 links, the other side. 
340 

.512 
510 



..250 
255 



Section I.) 
D 



LAND-SUKVEYING 



261 




In laying out the rectangle in the field, let A B represent the 
given side. At A, erect the perpendicular A D, which make = 
460.3 links ; and at B, erect the perpendicular B C, which 
make = A D. Then measure the line C D, and if you find it 
= A B, the work is right. 

2. If one side of a rectangle be 52.5 links ; required the other 
side, so that the figure may contain 6a. 2r. 23p. 

Ans. 1265.5 links. 



PROBLEM IV. 

To lay out any given Quantity of Land in a Rectangle, so that 
one of its sides shall be two, three, four, or any number of 
times as long as the other. 

Rule. — Divide the given area by the given number, and the 
square root of the quotient will be the shorter side, which multiply 
by the given number, and the product will be the longer side. 

EXAMPLES. 

1. Lay out 3a. Or. 32p. in the form of a rectangle, one of the 
sides of which shall be twice as long as the other. 

sq. links. 

3a. = 300000 
32p. = 20000 

2) 320000 

160000(400 links, the shorter side. 
16 2 

. . 0000 800 links, the longer do. 
s~3 



262 



LAND-SURVEYING. (Part VI. 



B 



D 



Let ABCD represent the rectangle, which you must lay 
out according to the directions in the last problem ; A D being 
800, and A B 400 links. 

2. A rectangle contains 7a. 2r. Op. ; what are its sides, one 
of them being three times the length of the other ? 

Ans. 1500 and 500 links. 



PROBLEM V. 

Upon a given Base, to lay out a Triangle that shall contain any 
given number of Acres, fyc. 

Rule. — Divide the area by half the base, or twice the area 
by the whole base, and the quotient will be the perpendicular 
of the triangle. 

EXAMPLES. 

1. Lay out 3a. 2r. 16p. in the form of a triangle, the base of 
which must be 1200 links. 



sq. links. 

3a. = 300000 

2r. = 50000 

16p. z= 10000 

6,00)3600,00 

600 links, the perpendicular. 



Section I.) land-surveying. 

C E 



263 




Upon any part of the given base A B, suppose at D, erect 
the perpendicular D 0, which make = 600 links ; then stake 
out the line A C and BC; so will A B C be the required tri- 
angle. But if the perpendicular be erected at either end of the 
base, as at B, then the line A E must be staked out ; and ABE 
will be the triangle required. 

2. Required the perpendicular of a triangle, which contains 
6a. 2r. 37p., its base being 1556 links. Ans. 865.2 links. 



PROBLEM VI. 

To lay out a Trapezium, that shall contain any Number of Acres, 
fyc. ; having one of its Sides or a base Line given. 

Rule 1. — Divide the given area into two parts, either equal 
or unequal ; and .then, by the last problem, find the perpen- 
dicular, that will lay out one of these parts in a right-angled 
triangle, upon the given base. 

You must then consider this perpendicular as one of the dia- 
gonals of the trapezium, and also the base upon which you 
must lay out the other triangle. 

Rule 2. — Divide the given area into any two parts, as before; 
and then, find the perpendicular that will lay out one of these 
parts in a right-angled triangle, upon the given base. 

Add the square of the perpendicular thus found, to the 
square of the given base, and the square root of the sum will 
be the hypothenuse. Consider this hypothenuse as one of the 
diagonals of the trapezium, and also the base upon which the 
other triangle must be laid out. 

84 



164 



LAND-SURVEYING. (Part VI. 



EXAMPLES. 

1. Lay out Ba. in a trapezium, upon a given side of 800 Kb 



BY THE FIRST RULE. 

I>i~:."r :he given :.: 5 and 3 acres, and let the triangle 

upon the given side contain th _ 

5a. =. 500000 square links. 
2 

1250 -..:-. :he perpendicular of the first triangle. 
I also the base of the - 
3a. = 300000 square links. 

_2 
125.0)600000(480 links, the perpendicular of the second 
500 triangle. 

1000 




In laving out the trapezium, in the field, let A B represent the 
given s:. if. A: B. a frpendicular B C. which make = 

1250 links. Then any part of the line B C. as ar I>. 

the perpendicular D E. vrhich make = 4> Kniks. Hi€ four out- 
line- -ill be completed. 



Section I.) land-surveying. 



265 



BY THE SECOND RULE. 



5a. = 500000 square links. 
2 



8,00)1000000 

1250 links, tlie perpendicular of the first triangle. 



Then, \/l250 2 + 800 2 = v 1562500 + 640000 =V2202500 

= 1484 links, the hypothenuse of the first, and also the base of 

the second triangle. 

3a. = 300000 square links. 
2 

1484)600000(404.3 links, the perpendicular of the 
5936 second triangle. 

• • 6400 
5936 

•4640 
4452 



188 



c 



13 



Having laid out the triangle A B C, as before directed ; upon 

any part of the line A C, as at D, erect the perpendicular D E, 

which make = 404.3 links. Stake all the outlines, and the 

work will be completed. 

2. Lay out 12a. in a trapezium, upon a given side of 1400 links. 

Ans. Supposing the given area divided into 7 and 5 acres ; 



266 land-surveying. (Part VI. 

then, by the first Rule, the perpendicular of the first triangle is 
found to be 1000 links ; and that of the second the same. 

By the second Rule, the perpendicular of the first triangle is 
found to be 1000 links ; the base of the second 1720.5, and its 
perpendicular 581.2 links. 



PROBLEM VII. 

Upon a given Base, to lay out a Rhomlus of any Content less 
than the Square of the Base. 

Rule. — Divide the content by the base, and the quotient will 
be the perpendicular. Then, from the square of the base, sub- 
tract the square of the perpendicular, and find the square root 
of the remainder. Upon the base, from one of its extremities, 
measure a line equal to this root, and at this point erect a per- 
pendicular. 

Note. — It is evident from the foregoing Rule, that the area of a rhombus 
or rhomboides may be found by multiplying the base by the perpendicular 
breadth. 

EXAMPLES. 

1. Lay out in a rhombus, 5a. 2r. 16p. its base being 800 links. 

sq. links. 

5a. = 500000 

2b. = 50000 

16p. — 10000 

8,00]5G00,00 

700 links, the perpendicular. 



Then, \/s00 2 - 700 2 =V 640000 - 490000=^150000=387.3 
links, at which distance, from one of the extremities of the 
base, the perpendicular must be erected. 

E C 



/ 



D B 



Section I.) land-surveying. 267 

In laying out the rhombus, in the field, let A B represent the 
given base. From A, on the line A B, measure 387.3 links to 
D ; and at D erect the perpendicular D E, which make =. 700 
links. At E, erect the perpendicular E C, which make = the 
base A B. Measure the lines C B and A E, and, if you find 
each of them = AB, the work is right. 

2. Lay out a rhombus, which shall contain 6a. 1b. 8p., upon 
a base measuring 900 links. 

Ans. The perpendicular is found to be 700 links, and the 
distance at which it must be erected from one of the extremities 
of the base 565.7 links. 

PROBLEM VIII. 

To lay out any given Quantity of Land in a Circle. 

Rule 1. — If we multiply the square of the diameter of any 
circle by .7854, the product will be the area ; consequently, if 
we divide the area by .7854, the quotient will be the square of 
the diameter. 

2. Multiply the square root of the area by 1.12837, and the 
product will be the diameter. 

EXAMPLES. 

1. Lay out one acre of land in a circle. 

sq. links. 
.7854)100000.000000(127323.65 links, the square of 
7854 the diameter. 

21460 
15708 

. 57520 
54978 



25420 
23562 

77s580 
15708 

. 28720 
23562 

.51580 
47124 

. 44560 
39270 



5200 



7i 



: : - vetey i 



1 



Or r bjtfeS 
X 1.1283? = 






: : . 






la laying oak tie eirde in. tie field- provide a strong end. in 

£if :-.:r-i:: A mi — _-_ — zzr A I 



— -J: ~i :i>i - -_:_ -:~ z.:-: 5tzi>t :~: -_t 
Oe^ at prefer mfcem!^ stretek die radios A B. 

:-i>T- ~ i~:l i n_zzr: i: - :': m "Jl-r 
9L Beqidredfhe Jmwmjh «f aeirefe, 





PROBLEM D 



-r ±i rilf _:, 



zi -1- 



.~i - 



Section I.) land surveying. 



269 



A Table of regular Polygons, with their Areas ; and the Radii of 

their circumscribing Circles, when the side of the Polygon is 1. 



1 No. 
Sides. 


Names. 


Areas. 


Radii. 


3 


Triangle 


0.433 


0.577 


4 


Square 


1. 


0.707 


5 


Pentagon 


1.72 


0.851 


6 


Hexagon 


2.598 


1. 


7 


Heptagon 


3.G34 


1.152 


8 


Octagon 


4.828 


1.306 


9 


Nonagon 


6.182 


1.462 


10 


Decagon 


7.694 


1.619 


11 


Undecagon 


9.365 


1.775 


12 


Duodecagon 


11.196 


1.932 



Note.—li the square of the side of any polygon, be multiplied by the area 
standing opposite to its name, in the preceding Table, the product will be 
the area of the polygon. 

EXAMPLES. 

1. Lay out one acre of land in a regular hexagon. 
100000 



HerG "2T98 



= 38491.147; and ^38491.147 = 196.191 



links, the side of the required polygon, and also 'the radius of 
the circumscribing circle, because the side of a regular hexagon 
and the radius of its circumscribing circle are always equal to 
each other ; hence the multiplier in the Table is 1. 



<>B 



270 land-suuveying. (Part VI. 

To lay out the hexagon, in the field, draw the circumscribing 
circle as directed in the last problem. Then, the radius A B, 
which is equal to the side of the hexagon, being applied six 
times, will just go round the circumference, and form the 
polygon required. 

2. Lay out half an acre of land in a regular octagon. 

Ans. The side of the required octagon is 101.76, and the 
radius of its circumscribing circle 132.898 links. 



PROBLEM X. 

To lay out any given Quantity of Land, in an Ellipsis, having 

one of the Diameters given. 

Rule. — If we multiply the rectangle of the two diameters of 
an ellipsis by .7854, the product will be the area ; consequently, 
if we divide the area by .7854, and that quotient by the given 
diameter, the latter quotient will be the diameter required. 

EXAMPLES. 

1. Lay out an ellipse, which shall contain one acre, with a 

transverse diameter of 450 links. 

sq. links. 
.7854)100000.00000(127323.6 quotient. 
7854 

21460 
15708 



57520 

54978 

• 25420 
23562 

• 18580 
15708 



28720 
23562 

•"51580 
47124 

• 4456 



Section I.) land-surveying. 

127323.G 



271 



Then, 



450 



z=. 283 links, the conjugate diameter. 




By Prob. 15, Part I., construct the ellipse ABCD; then by 
a property of the ellipse, (see my Mensuration, page 318,) the 
square of the distance of the focus from the centre, is equal to 
the difference of the squares of the semi-diameters : hence, we 
have v /225 2 -141.'5 i = v/ 30602.75 = 175 links, equal F o, or 
f o : and, 225-175 = 50 links, equal A F, or B f. 

Again, by another property of the ellipse, the sum of two 
lines drawn from the foci, and meeting in any point in the cir- 
cumference, is equal to the transverse diameter ; that is, F m -+- 
f m = A B. 

Procure, therefore, a cord, and upon it make two loops, so 
that the distance between them may be equal to the transverse 
diameter ; then measure, in the field, the diameter A B ; putting 
down a stake at each focus, and one at the centre o. At o, erect 
the perpendiculars o C and o D, making each = 141.5 links. 

Put the two loops over the stakes at F, f, and stretch the 
cord, so that the two parts F m, f m, may be equally tight ; at 
m put down a stake, as one point in the circumference of the 
ellipse ; and, in the same manner, determine as many others as 
you please. 

But if the ellipse be very large, so that you cannot conveni- 
ently procure a cord as long as the transverse diameter ; you 
must, then erect perpendiculars, called ordinates, at every 50 
links, or at every chain's length, &c. upon that diameter, and 
measure the lengths of these perpendiculars by the scale. 



272 laxd-suuvkying. (Part VI, 

Then measure, in the field, the transverse and conjugate dia- 
meters, and erect the perpendiculars in their proper places ; 
always remembering to put down a stake at the end of each 
perpendicular. 

2. Lay out an ellipse which shall contain 8a. 3r. 8 p., one of 
the diameters being given equal to 800 links. 

Ans. The other diameter is = 1400 links. 

Xote. — As Surveyors are frequently requested to lay out, in various 
figures, small quantities of land for plantations, &c. it is presumed that the 
foregoing problems will be found not without their use. 



PROBLEM XI. 

To part from a Square or Rectangle, any proposed Quantity of 
Land, by a Line parallel to one of its sides. 

Rule. — Divide the proposed area by the side upon which it 
is to be parted off, and the quotient will be the length of the 
other side of the figure required. 

EXAMPLES. 

1. From the square A B C D containing 6a. 1r, 26p., part 
off 3a. by a line parallel to A B. 




Section L) LAND-SURVEYING. 

sq. links. 

6a. = 600000 

1r. = 25000 

24p. = 15000 



273 



640000(800 links, the side of the square. 
64 

. . 0000 



— - 300000 ,. , . , . „ „ „ . , 

Then, = 375 links, the side A E, or B F required. 

800 



2. From the rectangle ABCD containing 8 a. 1r. 24p., part 
off 2a. 1r. 32p. by a line parallel to A D = 700 links. Then, 
from the remainder of the rectangle, part off 2a. 3r. 25p. by a 
line parallel to A B. 




sq. links. 

2a. = 200000 

1r. = 25000 

32p. = 20000 

7,00] 2450,00 

. 350 links, the side A E, or D F. 



sq. links. 

8a. = 800000 

1r. = 25000 

24p. = 15000 

7,00(8400,00 

1200lTnks, the side A B. 
350 the side A E. 

850 the difference = EB. 



2? 4 land-surveying, (Part VI. 

sq. links. 

2a. = 200000 

3r. = 75000 

25p. = 15625 

850)290625(342 links, the side E G, or B H. 
2550 

73562 
3400 



.1625 
1700 



3. Part off 6a. 3r. 12p. from a rectangle, containing 15a. bv 
a line parallel to the longer side ; the shorter being 1000 links. 

Ans. The longer side of the given rectangle is 1500, and the 
shorter side of the rectangle required is 455 links. 



PROBLEM XII. 



To part from a Square or Rectangle^ any proposed Quantity of 
Land, either in a right-angled Triangle or Trapezoid, by a Line 
drawn from any of the Angles to either of the opposite Sides. 

R rLF ,. — TThen the proposed area is to be parted off in a tri- 
angle, divide double this area by the base or side upon which it 
is to be parted off, and the quotient will be the perpendicular. 

When the proposed area is to be parted off in a trapezoid, 
subtract it from the area of the square or rectangle, and part off 
the remainder in a triangle, as above directed. 



EXAMPLES. 

1. From A B C D representing a square, whose side is 900 
links, part off a triangle which shall contain 2a. 1b. 36p. by a 
line drawn from the angle B to the side A D. 



Section I.) land-surveying. 
I> C 



275 




2 a. 1r. 36p. = 247500 square links. 
2 



9,0014950,00 

550 links, the perpendicular A E. 

Hence A B E is the triangle required. 

2. From A B C D representing a rectangle, whose length is 
1265,andbreadth 758 links, part off a trapezoid which shall contain 
7a. 3r. 24p., by a line drawn from the angle B to the side C D. 

D E 




A B 

sq. links. 

958870 the area of the rectangle. 

790000 ditto of the trapezoid. 

168870 difference, the area of the triangle. 
2 

758)337740(445.5 links, the perpendicular C E. 
3032 Hence A B E D is the trapezoid required. 
.3454 
3032 

.4220 
3790 



.4300 
3790 

.510 



T 2 



276 land-surveying. (Part VI. 

3. From a rectangular field, whose length is 1560, and breadth 
1000 links, it is required to part off a trapezoid, which shall 
contain 12a. 3r. 12p., by a line drawn from any of the angles 
to the longer opposite side. 

Ans. The area of the rectangle is 15a. 2r. 16p. j conse- 
quently, the area of the triangle is 2a. 3r. 4p., and its perpen- 
dicular 555 links. 

PROBLEM XIII. 

To part from a Triangle, upon the bam or longest side, any 
proposed Quantity of Land, by a Line drawn from either of 
the Angles at tfa I&fse, to the opposite Side. 

Rule. — Divide twice the proposed area by the base upon 
which it is to be parted off, and the quotient will be the per- 
pendicular. 

Or, if the proposed area be divided by half the base, the quo- 
tient will be the perpendicular. 

Note. — A Parallel Ruler may be used with advantage in this, and several 
of the following Problems. 

EXAMPLES. 

1. From ABC representing a triangle, whose base A Bis 1200, 
and sides A C and B C, 1000 and 800 links respectively, part off 
2a. 2r. 24p. by a line drawn from the angle B to the side A C. 




A D 

2a. 2r. 24p. = 265000 square links. 
2 

12,00)53001)0 

44l76 links, the perpendiculars D E. 



Section I.) land-surveying. 277 

At A, erect the perpendicular A F, which make = 441.6 links ; 
then draw F E parallel to A B, and it will intersect the side A C, 
in the point to which the division-fence B E must he made. 

Or, by the plotting-scale, erect the perpendicular DE = 441.6 
links, which will determine the point E. 

By the scale, you will find AE = 664 links ; measure, there- 
fore, in the field, 664 links from A to E ; stake out the line 
B E, and ABE will be the triangle required. 

• 2. From ABC representing a triangle, whose base A B is 1300, 
and sides B C and AC, 1100 and 900 links respectively, part off 
Ia. 3r. 36p. by a line drawn from the angle A to the side B C, so 
that the triangle A E C may contain the proposed quantity. 



From the three sides, b>y Note 4, Part IV., the area of the given 
triangle is found = 488076 square links. 
And,lA.3R. 36f. = 197500 square links. 
The difference = 290576, the area of the triangle ABE. 



1300)581152(447 links, the perpendicular D E. 
5200 

.6115 
5200 



.9152 
9100 
..52 



By the mode described in the last example, determine the 
point E, which you will find at the distance of 658 links from 
the angle B ; measure this distance in the field, from B to E, 
and proceed as before. 

t3 



278 land-surveying. (Part VI. 

3. From a triangular field, whose sides are 1500, 1200, and 
1000 links respectively, part off 3a. 2r. 16p. by a fence made 
from the greater angle at the base, to the opposite side. 

Ans. The perpendicular of the triangle required, is found to 
be 480 links ; and it rises upon the base, at the distance of 537 
links from the less angle. 



PROBLEM XIV. 

To part from a Triangle, any proposed Quantity of Land, by a 
Line parallel to any one of its Sides. 

Rule. — The areas of similar triangles are to one another in 
the duplicate ratio of their homologous sides : hence, as the area 
of the triangle A B C is to the square of the side A C, or B C, 
so is the area of the triangle D E C to the square of the side 
DC or E C respectively. (See Theo. 13, Part I.) 




EXAMPLES. 

1. Suppose the base A B = 1200, the side A C = 1000, and 
the side B C = 800 links; part off 1a. 2r. 16p. by the line 
D E parallel to A B. 

From the three sides, by Note 4, Part IV., we find the area 
of the triangle. 

ABC = 396863 square links. 

And, I a. 2r. 16p. = 160000 square links. 

The difference = 236863, the area of the triangle DEC. 



Section I.) land-surveying. 279 

Then, as 3968G3 : 1000 X 1000 :: 236863 : 596838.20; and 
V 59683^20=772.5 links =DC; hence 1000 - 772.5=227.5 
links=AD. Again, as 396863 : 800x800 :: 236863 : 381976.45; 
and v/ 38 1976*45 = 618 links = EC; then 800-618 = 182 
links = B E. 

Measure, therefore, in the field, 227.5 links from A to D ; and 
from B to E measure 182 links ; stake out the line D E, and 
the work will be completed. 

2. From a triangular field, whose sides are 1800, 1500, and 
1200 links respectively, part off 3a. 2r. 32p. by a line parallel 
to the shortest side. 

Ans. The area of the given triangle is 892941 square links ; 
the area of the triangle made by the line of division is 522941 
square links ; and one of its sides, from the angle opposite the 
line of division, to the commencement of that line, is 1147.9, 
and the other 1377.4 links. 



PROBLEM XV. 

To part from a Rectangle or Triangle, any proposed Quantity 
of Land, upon a Line on which there are Offsets, when the 
Area of those Offsets is to be considered as Part of the Portion 
to be parted off. 

Hule. — Find the area of the offsets, which subtract from the 
portion to be parted off, and then proceed with the remainder, 
as directed in the preceding problems. 

But, in a rectangle, when there are offsets on one, or both of 
the lines adjoining that upon which the given quantity is to be 
parted off, reject these offsets, and proceed as before directed. 

Then, having found the distance at which the line of division 
must be from that upon which the given quantity is to be parted 
off ; find the area of the offsets contained between those lines, 
which area divide by the latter line ; and the quotient will be 
the distance by which the former line must be approximated to 
the latter. 

x 4 



280 



LAND-SURVEYING. (Part VI. 



EXAMPLES. 

1. From a rectangular field, whose dimensions are contained 
in the following notes, part off 2a. 3r. 32p. upon the chain-line 
A B, so that the offsets taken upon that line may be included. 



Begin 



DA - 




560 




L. off D. 




CD 




1200 




1000 




L. off C. 




BC 




560 




L. off B. 




A B 




1200 





1000 




900 


60 


600 


SO 


300 


50 


000 





at A. 


Range E 




sq. links. 
2a. 3r. 32p. = 295000 

57000 the area of the offsets. 
1 2,00 1 23807>0 the difference. 

198.4~links = A E, or B F. 



Hence the irregular figure, A G B F E, contains 2a. 3r. 32p. 



Section I.) land-surveying. 281 

2. From a rectangular field, whose dimensions are contained 
in the following notes, part off 2a. 2r. 8p. by a line parallel to 
the chain-line AB; so that the offsets taken upon this line, and 
also those upon the two adjoining lines, contained between the 
chain-line A B and the line of division, may be included. 





DA, 





500 


40 


350 


55 


250 


45 


150 





000 




R. off D. 




CD 




1000 




R. off C. 




BC 





500 


40 


400 


60 


250 


45 


150 





000 




R. off B. 




AB 





1000 


50 


700 


70 


450 


40 


200 





000 


Begin 


at A. 



Range W. 




282 land-surveying. (Part VI. 

sq. links. 
2a. 2r. 8p. = 255000 

_40250 the area of the offsets taken on A B. 
1 ,00 01214 750 the difference. 

214.750 links = BaorAm, which we may 
call 215 links. Now 215 - 150 = 65 = r a = c m ; and, by 
the scale, a e is found to measure 58, and m n, 53 links ; hence 
the area of the offset B a e + the area of the offset A m n = 
13282, which divided by 1000, gives 13 links, the distance by 
which the line e n must be approximated to A B. Conse- 
quently, E F is the true line of division ; and the irregular 
figure A G B E F contains 2a. 2r. 8p. minus the two shaded 
offsets. 



PROBLEM XVI. 

To part from a Trapezium, or any irregular Polygon whatever, 
any proposed Quantity of Land, by a Line drawn parallel to 
any of the Sides, or by a Line drawn from any of the Angles, 
or from any assigned Point in one of the Sides, to any of the 
opposite Sides. 

Rule 1 . — Having laid down the whole figure, draw a guess- 
line in the direction required, parting off, as nearly as can be 
judged, the proposed quantity ; after which, by the scale, mea- 
sure, with the greatest accuracy, the guess-line, and also the 
quantity thus parted off. 

Then, if the guess-line or line of division be drawn from an 
angle, or from any assigned point in a side, divide the difference 
between the proposed quantity and the quantity parted off, by 
half the guess-line, and the quotient will be the perpendicular 
to be set off, on one side, or the other, of the guess-line, accord- 
ingly as the quantity parted off is more or less than the quantity 
proposed. To the end of this perpendicular, from the point 
assigned, draw a new line of division ; and it will part off the 
quantity required. 

2. But if the guess -line be drawn parallel to any of the sides, 
divide the difference before mentioned, by the whole guess-line, 



Section 1.) land-surveying. 283 

and the quotient will be the perpendicular to be set off from 
each end of the guess-line, on one side, or the other, as above. 

Note 1. — When from a trapezium, approaching very nearly to a rect- 
angle, it is required to part off any number of acres, &c. by a line parallel 
to one of its sides ; it may be done as directed in Prob. XI. ; and if there 
be offsets upon any of the lines, they must be treated as in the last Problem. 

2. — In using guess-lines, it is not necessary that the learner should draw 
them so as to coincide in measure, with those of the examples which he is 
performing. It will be sufficient for him to proceed in a similar manner. 



EXAMPLES. 

1. From a trapezium, whose dimensions are contained in the 
following notes, part off 2a. 2r. 24p. by a line parallel to the 
side A B. 



Return 



Begin 



BD 

1249 
1000 
toB. 

1112 

1000 

R. off A. 



D A 

550 
R. off D. 



CD 

979 
R. off C. 



BC 
557 
R. off B. 



AB 

1114 
1000 
at A. 



Diag. 



Diag. 



Range W. 



284 



LAND-SURVEYING. 



(Part VI. 




Having laid down the figure, draw the guess-line m n parallel 
to A B ; and from n, let fall the perpendicular a n ; then, sup- 
pose m n = 1058 links, a n will be = 230, and A a = 1052 
links; therefore, Ba = 1114 -1052 = 62 links, 
sq. links. 

Then, 1055x230 = 242650 the area of the trapezoid A a n m. 

And, 230x 31= 7130 the area of the triangle Ban. 

The sum - =249780 the area of the trapezium A Bnm. 
2a. 2r. 24p.=265000 

15220 the difference between the quan- 
tity proposed, and the quantity parted off by the guess-line ; 
which, divided by 1058, gives 14.4 links, to be set off perpen- 
dicularly from m and n toward D and C. Hence, E F is the 
true line of division ; and the trapezium A B E F contains 2a. 
2r. 24p. 

As A is very nearly a right-angle, measure, in the field, 230 
-f- 14.4 = 244.4 links, from A to F. Then, upon any part of 
the line A B, (toward B) as at e, erect the perpendicular e r, 
which make = 244.4 links ; stake out the line E r F, and the 
work will be completed. 

2. From a trapezium, whose dimensions are contained in the 
following notes, part off, in a triangle, Ia. 3r. 12p. by a line 
drawn from the angle C to the side A B. 



Return 




Diag. 



Section I.) land-surveying. 



285 




Having laid down the figure, draw the guess-line C m, which 
suppose = 638 links. From m let fall the perpendicular m a, 
which will be = 417 links. 

sq. links. 
Then, 410 X 417 = 170070 the area of the triangle BCm. 
1a. 3r. 12p. = 182500 

11530 the difference between the 
quantity proposed, and the quantity parted off by the guess- 
line, which is divided by 319 (half the guess-line) gives 36 links, 
to be set off from m toward A. Hence, E C is the true line of 
division ; and the triangle B C E contains 1a. 3r. 12p. 



286 land-surveying. (Part VI. 

Also, A E is found =731 links : measure, therefore, in the 
field, 731 links from A to E; stake out the line E C, and the 
work will be completed. 

Note. — The Rules given in this problem, for parting off land from irregu- 
lar figures, are generally adopted by Practical Surveyors ; because they 
may be applied to any irregular figure whatever. Land, however, may 
sometimes be parted off more directly : for instance, the foregoing exam- 
ple may be performed by the mode followed in Prob. XIII., i. e. if the 
given quantity, in square links, be divided by half the line B C, the quotient 
will be the perpendicular of the triangle BCE; then, at the distance of 
this perpendicular, a line drawn parallel to B C, will intersect the line A B 
in E, the point to which the division-fence must be made. 

3. From a field, whose dimensions are contained in the fol- 
lowing notes, part off 3a. 2r. 1 6p. toward A D, by a fence made 
from the side A B to the side C D, so that the fence may com- 
mence at the distance of 600 links from A. 



Return 


BD 

1050 
to B. 




AC 

1708 

1000 

L. off A. 




DA 

790 
L. off D. 




CD 

1130 
1000 

l. off a 




BC 

640 
L. off B. 


Begin 


AB 

1320 
1000 
at A. 



Diag. 
Diag. 



Range E. 



Section I.) land-surveying. 



287 




Having constructed the figure, set off 600 links from A to E, 
and draw the guess-line E m, which suppose — 702 links ; the 
diagonal A m will be = 1 132, the perpendicular Daz: 278, and 
the perpendicular E a = 318 links. Hence, the area of the 
trapezium A D m E, is found =: 337336 square links ; but the 
quantity proposed (360000 square links) exceeds the quantity- 
parted off by 22664 square links : this divided by 351 (half the 
guess-line) gives 64.5 links, to be set off from the line E m, per- 
pendicularly toward B C. 

Now, continue the line E m, and upon it erect the perpen- 
dicular nF = 64.5 links. The line F E will be the true line of 
division; and the trapezium ADFE contains 3a. 2r. 16p. 

If it had been required to set off the perpendicular on the 
other side of the line E m, you must still have erected it so that 
its end might have touched the line C D. 

Now, by the scale, D F is found = 553 links. Measure, there- 
fore, in the field, 600 links from A to E, and 553 from D to F ; 
stake out the line F E, and the work will be completed. 

Note. — The last example may also be performed by finding the area of 
the triangle A D E, and subtracting it from the given quantity ; then, if 
the remainder be divided by half the line D E, the quotient will be the per- 
pendicular of the triangle D E F. 



288 



LAND-SURVEYING. (Part VI % 



At the distance of this perpendicular, draw a line parallel toDE; and it 
will intersect the line C D in F, the point to which the division-fence must 
be made. 

4. From an irregular field, whose dimensions are contained in 
the following notes, part off 2a. 3r. 20p. toward the line A E, 
by a fence made from the angle D to the side A B. 





EB 




1398 




1000 




R. off E. 




CE 




1240 




1000 




500 




R. off C. 




AC 




1260 




1000 




R. off A. 




E A 





400 


80 


200 





000 




R. offE. 









DE 





600 


25 


450 


35 


300 


20 


150 





000 




R. off D. 




CD 




740 




R. off C. 




BC 




550 




R. offB. 



Diag. 



Diag. 

m, proof-line, goes to D, 
and measures 324. 



Diag. 



Section I.) land-surveying 



289 





AB 





1250 


35 


1000 


50 


800 


60 


600 


50 


400 


30 


200 





000 


Begin 


at A. 



Range W. 




H J 1 



the area of the offsets taken 
on the different lines. 



Having laid down the figure, draw the guess-line D n, which 

suppose = 766 links ; then the diagonal A D will he = 824, 

the perpendicular Ea = 278, and the perpendicular r a = 372 

links ; r e also will be = 228, and r n = 52 links. 

sq. links. 

267800 the area of the trapezium ArDE, 
12000) DE(,? 
16000 EA " 
123 48 j A r { 

308148 the area of the irregular figure A n D E. 
2a. 3r. 20p. z= 287500 

20648 the difference between the quantity 

proposed, and the quantity parted off by the guess-line, which 

divided by 383 (half the guess-line) gives 54 links, to be set 

off from n toward A. Hence, D F is the true line of division; 

and the irregular figure A F D E contains 2a. 3r. 2 Op. 

u 



290 land-surveying. (Part VI. 

Now, by the scale, A c is found = 377 links. Measure, 
therefore, in the field, 377 links from A to c; stake out the 
line D c F, and the work will be completed. 

Note 1. — If the area of the irregular figure A D E, be subtracted from the 
given quantity, and the remainder divided by half the bine A D ; the quotient 
will be the perpendicular of the triangle A D F ; the side A B being nearly 
straight from A to F, 

Now, at the distance of this perpendicular, draw a line parallel toAD ; 
and it will intersect the side A B in F, the point to which the division- 
fence must be made. 

2. — It is not absolutely necessary to survey and plan a whole field, in 
order to part a portion from it, as the guess-line and portion parted off may 
be measured in the field ; but, in my opinion, the former, in general, is a more 
eligible method than the latter ; as you have a better opportunity of proving 
vour work. 



SECTION II. 

THE METHOD OF DIVIDING A PIECE OF LAND AMONG 
SUNDRY CLAIMANTS, IN THE PROPORTION OF THEIR 
RESPECTIVE CLAIMS, OR A COMMON, §c. OF VARIABLE 
VALUE, AMONG ANY NUMBER OF PROPRIETORS, IN 
THE PROPORTION OF THEIR RESPECTIVE INTERESTS. 

"When land becomes the property of coheirs, copartners, joint 
purchasers, &c. it is generally divided into such shares, as the 
coparties are entitled to ; and this cannot possibly be accurately 
effected without the assistance^ of some person, who is not only 
well acquainted with surveying, but also with the method of 
dividing land. 

In this process an error is evidently much more material than 
one committed in surveying. — When a field, &c. is to be di- 
vided into any number of parts, equal or unequal, it is neces- 
sary, first, to ascertain its dimensions ; and next to inquire of 
the parties concerned, in what part of the property in question, 
they wish their respective shares to lie. 



Section II.) land-surveying. 



291 



PROBLEM I. 

To divide a Square or Rectangle, either equally or unequally, 
among any Number of Persons, by Lines parallel to one of 
its Sides. 

Rule. — If the parts, into which the field is required to he 
divided, he equal, divide the side which will he cut hy the di- 
vision-fences, hy the numher of those parts, and the quotient 
will be the distance at which the division-fences must be placed 
from each other, and from the outsides to which they are pa- 
rallel. But, if the parts be unequal, you must then part off 
each person's share as directed in Sect. I. Prob. XI. 



EXAMPLES. 

1 . Divide the square A B C D containing 5a. 2r. 20p. into 
three equal parts, by fences parallel to the side A B. 

C 




B 



Here 5a. 2r. 20p. =562500 square links; and *J 562500 = 
750 links, the side of the square. This, divided by 3, the num- 
ber of parts, gives 250 links, the distance at which the first di- 
vision-fence must be placed from A B, &c. From A and B, 
therefore, set off 250 links to E and F; join E F, and the rect- 
angle A B F E, will be one of the parts required. 

u 2 



292 land-surveying. (Part VI. 

Again, from E and F set off 250 links to G and H ; join 
G H, and the rectangles E F G H, and G H C D will be the 
two other parts required. 

2. Divide ABCD representing a rectangular field, whose 
length is 1500, and breadth 800 links, among three men, A, B, 
and C, by fences parallel to the side A D, so that A may have 
3a. B 4a. and C the remainder. 
D F H C 




EG B 

Here 3a. = 300000 square links, which divided by 800, 
gives 3? 5 links = A E or D F : hence the rectangle A E F D 
contains A's share. 

Again, 4a. = 400000 square links, which divided by 800, 
gives 500 links — E G or F H : hence the rectangle E G H F 
contains B's share. 

Xow, the rectangle A B C D, is found to contain 12a. ; con- 
sequently, the rectangle GBCH containing 5a. is C's share. 

Note. — This and similar examples may also be performed by the following 
proportion : As the area of the whole rectangle is to the whole base, or side 
cut by the division-fences, so is each person's share of the rectangle to his 
share of the base. 

PROBLEM II. 

To divide a triangular Field, either equally or unequally, among 
any Number of Persons, by Fences made from any of its 
A nales to the opposite > 
Rule. — If the parts, into which the field is required to be 



Section II) land-surveying. 293 

divided, be equal, divide the base, or side to which the division- 
fences are to be made, by the number of those parts, and the 
quotient will be each persons share of the base. But, if the 
parts be unequal, say, as the area of the whole triangle is to the 
whole base, so is each person's share of the triangle to his share 
of the base. (See Simpson's Geom. IV. 7. ; Reynard's Geom. 
V. 1. ; and Euclid VI. L) 



EXAMPLES. 

1. Divide ABC, representing a triangular field, whose sides 
A B, A C, and B C are 1500, 1200, and 1000 links respectively, 
into three equal parts, by fences made from the angle C to the 
side A B. 




Here AB= 1500 links, which divided by 3 (the number of 
parts) gives 500 links, each person's share of the base. From 
A, therefore, set off 500 links to D, and from D 500 links to 
E ; draw the lines C D and C E, to represent the division- 
fences ; and the triangles A D C, D E C, and E B C, are the 
three equal parts required. 

2. Divide ABC, representing a triangular field, whose sides 
A B, A C, and B C are 1450, 1150, and 960 links respectively, 
into three equal parts, by fences made from the angle A to the 
side B C. 

u 3 






"d-subvey: 



ri VL 




parte) gh-es 920 links, eack person's dare tf Ike side B C. 
From B, tneref are, set off 320 finla - I . and fiwD set off 



Dhide A B C, representing a triangular field, 

A 1 A C. iii I I :: T .. 




Section II.) LAND-SURVEYING . 295 

Having the three sides of the triangle, we find its area 
= 1272792.2 square links; then, as 1272792.2 : A B = 2200 
:: A's share = 300000 square links : 518.5 links, A's share of 
the base. 

Again, as 1272792.2 : 2200 :: 400000 : 691.3 links, B's 
share of the base. 

The remainder of the base, which is 990.2 links, belongs to 
C ; and, deducting 7a., the sum of A and B's shares, from the 
area of the whole triangle, we find remaining for C's share 
572792.2 square links = 5a. 2r. 36p. 

From A, therefore, set off 518.5 links to D, and from D set 
of 691.3 links to E ; and the lines CD and C E will be the 
lines of division required. 



PROBLEM III. 

To divide a triangular Fields either equally or unequally, among 
any Number of Persons, by Fences proceeding from any as- 
signed Point in one of its Sides. 

Rule. — Divide the base or side of the triangle from which 
the division-fences are to be run, as directed in the last problem. 
From the assigned point, draw a line to the opposite angle ; 
and parallel to this line, draw a line from each point of division 
on the base, until it intersects the opposite side. From these 
points of intersection draw lines to the point assigned ; and 
they will be the lines of division required. (See Dr. Hutton's 
Course of Mathematics, Vol. III. Chap. 7, Prob. 2.) 

EXAMPLES. 

1. Divide ABC, representing a triangular field, whose sides 
A B, B C, and A C are 1500, 1150, and 950 links respectively, 
equally among three persons, by fences proceeding from a gate, 
700 links distant from A on the base, leading into a lane, 
through which alone a road can be had to the field. 

u 4 



296 



LANL-SURVEYIV - 



Pari VI 




he question AB = 1500 links, divided by 3, grres 500 

I •'-'-'?. -:.\'l '::■::.- ~_:f :: :~_t i-z F::z A. :!:::::::. ^: 
z~ ■:'.'. ~ >> :: I iii f::n I —: :z ":"_.- z: :; E. 

TlrZ fr.zi Tie _ -. !t '. :lr Li^r G C: i^E ririllfl :•:■ ::. 
Ike Hues D H and E F. E: ::~ E -id F draw the lines H G 

cm x G\ n. . "_r~ ""'. t zjLr :t~:t- :: :^~.«: z :•: 

N ~. j b juilar triangles, (Theo. 11. Part L) as A G : A C : 

AD:AH = :^.:Eis:-:. E 1:B( 3E:BF 

= Tlf "'"Vs. Measure, therefore, in the field, 6T8.5 links 

from A to H. and 71S.7 from B to F : stake ont the tines H G 

.. 7 >. z -jl ■ \: ". ' . : 



mler, the fines A H and B F may he 






l _':— if A B C. ~i^~m--zz.z i :nizrEir ~-\i. ~i:fr iiif* 
A B. A C. ni B C are 1400, 1200, and 1000 Knks respeciiTelT. 
among dree persons. A _ md C. by fences proceeding from a 
pond which is at the distance of 600 links from A on the base ; 
so that each person partaking of the pond, A may have 1 acre, 
2 roods, and 10 perches ; B I acxe, 3 roods, and 20 perches; 
and C the remainder. 



Section II) land-surveying, 



297 




Having the three sides of the triangle, we find its area = 
587877.5 square links. Then, as 587877.5 : A B = 1400 :: 
A's share == 156250 square links : 372 links, his share of the 
base. 

Again, as 587877.5 : 1400 :: 187500 : 446.5 links, B's 
share of the base. 

From A, therefore, set off 372 links to D, and from D set off 
446.5 to E. Then from the pond P draw the line P C, and 
parallel to it, the line D G and E F. From G and F draw 
the lines G P and F P ; and the triangle A P G will contain 
A's share ; the trapezium P G C F, B's share ; and the triangle 
B P F, C's share = 244127.5 square links = 2 acres, 1 rood, 
and 30 perches. 

By similar triangles, we find A G — 744, and B F = 726.8 
links : proceed, therefore, in the field, as directed in the last 
example. 



PROBLEM IV. 

To divide a triangular Field, either equally or unequally, among 
any Number of Persons, by Fences made parallel to one of its 
Sides. 

Rule.— By the rule given in Sect. I. Prob. 14, part off the 
first person's share ; proceed with the remainder of the triangle, 



:*5 i rEYB P • : r/. 



A B, A C. and B C are 1500, 1300, aai 1000 fiats itay ttt liit s lj ; 






tt- 



_■ 



_:_ l_~ iri "•_- ?. _--- : . . ~_ ; 5 _■!_•_- - '.-- Vi : : r .:- 

::':lr -- — A I G 

~: = :::, * iriis = a E 

Arn^ as 59S11&4 : 1200 X ISO* : 960000; and 

n ~ = Vr ? ^ZlVf - A G 

lz ■• T* iJ ~r = - znVs - A I 

and ^4800OM>2 = 6&2.S Knks = AF. Hasce, the liim^V 
ABC is divided ioto tferee equal par 



Section II.) land-surveying. 299 

2. Divide ABC, representing a triangular field, whose sides 
A B, B C, and A C are 2200, 1700, and 1500 links respectively, 
among three persons, A, B, and C, by fences made parallel to 
the base A B, so that A may have 3a. B 4a. and C the re- 
mainder. 




The area of the triangle A B C is found = 1272792.2 square 
links, from which taking 300000 square links, (= A's share) 
we leave 972792.2 square links, the area of the triangle D G C 
From this taking 400000 square links, (= B's share,) we leave 
572792.2 square links, the area of the triangle EFC = 5a. 2b 
36p. = C's share. 

Then, as 1272792.2 : 1700 x 1700 :: 972792.2 : 2208820.46 
and ^2208820^46 = 1486.2 links = CG. 

And, as 1272792.2 : 1500 X 1500 :: 972792.2 : 1719669.91 

and ^1719669^91 = 1311.3 links = CD. 

Again, as 972792.2 : 1486.2 x 1486.2 : : 572792.2 : 1300563.40 

and J 1300563.40 = 1140.4 links = CF. 

And, as 972792.2 : 1311.3 x 1311.3 :: 572792.2 : 1012467.60 



and ,y 1012467.60 = 1006.2 links = CE. Hence, the triangle 
A B C is divided into three parts, as required. 



300 



LAND-SURVEYING. 



(Part VI. 



PROBLEM V. 

To divide a Trapezium, or an irregular Polygon, equally or un- 
iffjr, among any number of P .ces made in a 

turn. 

Rrc.E. — By the Rules given in Sect. I. Prob. 16, part off the 
first person's share ; proceed with the remainder of the figure 
and the second persons share in the same manner ; and thus 
continue, till the whole figure is divided. 

EXAMPLES. 

1. Divide a trapezium, whose dimensions are continued in 
the following notes, into three equal parts, by fences made from 
the side A B to the side C D. 



BD 
1.542 

Return to B, 



A C 

1848 
U 

R. off A. 



DA 

91.5 

R. offD. 



C D 

1347 

1000 

R. off C 



B C 

885 

R. off B. 



Begin at 



AB 
1547 

1000 
A. Range 



Diag. 



Diag. 



W. 



Section II) land-surveying, 



301 



mF 



xiH 



jy 





,/""] 




.■••, i 


\ 


\ 


1 


&i 


W 


\ 


I- - 


\ ' 






3 \ 



B 



G 



The area of the triangle A B C, is found = 681942, and the 
area of the triangle CDA = 585949 square links ; consequently, 
the area of the trapezium ABCD = 1267891 square links, which 
divided by 3, gives 422630 square links, for each person's share. 
Now, draw the guess-line E m, which suppose = 880 links ; 
then the diagonal E C will be found = 1028, the perpendicular 
Ba = 387, and the perpendicular m a = 424 links : hence, the 
area of the trapezium B C m E, is found s= 416854 square links^ 
which is too little by 5776 square links. This divided by 440 
(half the guess-line) gives 13 links, to be set off from m toward 
D ; consequently, E F is the true line of division. 

Again, draw the guess-line G n, which suppose = 878 links ; 
then will the diagonal G F = 1017, the perpendicular Ear 
430, and the perpendicular n a — 385 : hence, the area of the 
trapezium E F n G, is found = 414427 square links, which is 
too little by 3203 square links. This divided by 439 (half the 
guess-line) gives 19 links, to be set oft' from n toward D ; con- 
sequently, G H is the true line of division ; and the trapezium 
A B C D is divided into three equal parts, as required. 

Now, by the scale, we find BE=: 450, EG=500,CF = 508, 
and F H = 468 links, which distances must be measured in the 
field, in order to determine the situations of the division-fences. 



B02 



LAXD-SUKVEYIXG, 



(Part VI. 

Note. — If we subtract the area of the triangle B C E, from the quantity to 
which each person is entitled, and divide the remainder by half the line C E, 
the quotient will be the perpendicular of the triangle C E F. By drawing a 
line parallel to C E, at the distance of this perpendicular, the point F may be 
determined. 

In a similar manner, may be parted off the trapezium E F H G. 

2. Divide a field, -whose dimensions are contained in the fol- 
lowing notes, among three persons, A, B, and C, so that each 
partaking of a pond at P, A may have 3a. B 4a. and C the 

remainder. 



BD 




1447 


Diag. 


1000 




R. offB. 




EB 




1603 


Diag. 


1000 




ft. off E. 




CE 




1300 


Diag. 


1000 




R. off C, 




AC 




1320 


Diag. 


1000 




700 


Pond. 


R. off A. 




E A 




750 




R. offE. 




DE 




650 




R, offD. 




CD 




850 




R. off C. 








BC 




800 




R. offB. 




— 





Section II.) land surveying. 



303 



Begin 



AB 

1200 

1000 

at A. Range 



W. 




From the pond P, draw the line P D, and also the gness-line 
P m, which suppose = 558 links ; then will the diagonal D m 
he = 1025, the perpendicular Par: 400, and C a = 195 links : 
hence, the area of the trapezium P m C D is found = 304937 
square links, which exceeds A's share by 4937 square links. 
This divided by 279 (half the guess-line) gives 17.7 links, to be 
set off from m toward C ; consequently, P F is the true line of 
division, and the trapezium P F C D contains A's share. 

Again, draw the guess-line P n, which suppose. = 696 links ; 
then, the diagonal P E will be = 848, the perpendicular n a = 
247, and D a = 552 links : hence, the area of the trapezium P n 
E D, is found = 338776 square links, which is less than B's 
share, by 61224 square links. This divided by 348 (half the 
guess-line) gives 176 links, to be set off from the line P n per- 



304 LAND-SUB TRYING. PmWt VI. 

pendicularlr toward A iie true line of 

nd the trapezium P G E D con- hare. 

irregular polygon A B F P G c :-:_:_- <L - : _ r 
which will be found = 4a. Sr. 1 

fond = . . and B F = 545 links, 

which distances must be measured in the field, in order to de- 
termine the situations of the dhisi i t-fiama. 

L — Theforegoing example ma y also be performed by subtracting the 
area of the triangle C D P from A*s share ; and then laying out the re- 

i-innlr: _ ±i -:._:-_ ! 7 7. .- : ., 1_ r :: = 1 
In a similar manner, may he parted off B's sL n 

. — ~ae division of the last, or any other figure, may be proved by finding 

- ..- ;;- :::jir ~7:.t rrire. -ju:z. .:' r_.:7. : n^:. f :/-_l! :■: :'"r r~- ::' 
:'-t ir-ri? ::' -ir : ir: : '__ :: ---"-.::'„;: "_ - - '-: L~ iri. 1t~ : :. -7 .— -- - - .:■: 

■- :e :~._v.- 



PR : BLEM VI. 

;wjw#ii, or any quantity of Zand, of «r 
ValH.\ among amy mnmber of Proprietor*, in the proportion 
of their respective Interests. 

ais ease, the land to be divided must first be 
and next, the estate of each propriet: be un- 

known. Then, if it be required to make the dirision according 
to the Talue of each person s estate, there must be proper per- 

ppointed to Talue them, which, in this Problem, w 
suppose, may be done a: so much per acre, uniformly, through- 
out each estate. 
■ 

: — '":.-. l :1=. ... - : .. . .r - :: _.:.:~.:. " :- i:\ - - -" 
hi wanted than its quantity . 

I: is immaterial whether the land be Tamed at 5s. or 5L per acre, if 
the same proportion, according to the quality of the land, &c. be observed 
in valuing each person's estate. 



Section II.) LAND-SURVEYING. 805 

To determine each Person's share. 

Rule. — As the number of acres, &c. contained in the sum of 
the estates, is to the whole quantity of land to be divided, so is 
each person's estate to his respective share. Or, as the sum of 
the values of all the estates, is to the whole quantity of land to 
be divided, so is the value of each person's estate to his re- 
spective share. 

EXAMPLES. 

1. Divide a common containing 56a. 2r. 16p. among three 
persons, A, B, and C, whose estates are 58, 96, and 128a. 
respectively. 

Here 58+96+128=282, the number of acres contained in all 

the estates ; and 56a. 2r. 16p. = 5660000 square links. Then, 

a. sq. links. A. R. p. 

A. sq. links. ( 58 ] ( 1164113 ] (112 22.5 ) A's ) 6 



as282:5660000 ::{ 96 V .V 1926808 \ — l 19 1 2.8 >B's V % 
128 2569078 25 2 30.5 C's * ^ 



5659999 56 2 15.8 proof. 

Each person's share thus determined, the common may easily 
be divided by the methods already described, 

2. Three gentlemen, A, B, and C, have each an estate consist- 
ting of 300a. ; divide among them, according to the values of 
their estates, 75a. 3r. 32p. ; A's estate being valued at 25s., B's 
at 32s., and C's at 40s. per acre, per annum. 



(25) ( 7500 the value of A's estate. 
Here 300 X < 32 V = ^ 9600 ditto of B's. 
( 40 ) [ 1 2000 ditto of C's. 

29100 sum. 



And 75a. 3r. 32p. = 7595000 square links. Then, 

s. sq. links. a. r. p. 

s. sq. links. ( 7500 ) ( 1957474 ) ( 19 2 12 ) A's ( <- 

a829100:7595000::-< 9600 V : <( 2505567 V = <^ 25 9VB's^S 
( 12000 j ( 3131958 ) ( 31 111 j C's {-% 

7594999 75 3 32 proof. 



306 land-surveying. (Pari VI 

Note. — It sometimes happens that two, three, or more persons join in 
taking a common pasture, and agree to pay in proportion to the number of 
cattle with which each person depastures. In such cases, when the whole of 
the cattle graze an equal time, you must make use of the rule of Single 
Fellowship, by saying, as the whole of the cattle, is to the rent of the whole 
parture,so each person's cattle to his share of the rent. But when the cattle 
graze an unequal time, you must then have recourse to the rule of Double 
Fellowship, \ ; f the products of each person's cattle 

and time, is to the whole ren- :li person's product to his share of 

the rent. 



PROBLEM VII. 

To divide a Gammon, . if :irioble Value, among any numher 
of Propr. :\e Pro p or ti on to their respective I 

In a work of this kind, the quantity of every different quality 
is required, not only of the land to be divided, but also of each 
proprietor s estate ; consequently, the Surveyor, accompanied by 
the persons appointed to value, generally called 4i Commis- 
sioners." must examine each persons estate, and also the Com- 
mon, previously to the survey being taken. 

In doing this, they must stake out lines between the different 
qualities of the soil ; and. in surveying, these lines (called by 
Surveyors, " Quality-lines") must be considered as boundaries, 
and represented in the field-book, and upon the plan, by small 

By way of distinction, there ought to be two stakes put down 
at each angle formed, by the quality-lines : and also marks cut 
in the ground, pointing in the direction of these lines, so that 
if the stakes should be pulled up, thesr marts maj serve as 
directors. 

When the survey is finished, and laid down, every different 
quality. re] resented upon the plan, must be sot num- 

bered, 1, 2, -3, Sec The Sti rr eyor must then require the Com- 
missioners to put the different valuations upon the land ; and, 
in doing this, he must accompany them with the plan, in order 
that both he and they may know the ground corresponding 
with each number. Surveyors generally asc letters to repre- 
sent the different values of land : 



Section II) land-surveying. 307 

Thus, a, may denote 1 shilling. 

b 2 

c 8 

d 4 

e 5 

f 6 

g 7 

h 8 

i 9 

o 10 

s 20 

and x 30 shillings. 

By putting three of these letters together, and adding their 
separate values, the value per acre per annum, may he set down 
as high as sixty shillings ; and, hy adding more letters, it may 
be carried to any height required. By the use of these letters 
the confusion, arising from a multiplicity of figures, is avoided. 

The land being valued, you must then proceed to find the 
quantity contained under each number on the plan ; and also 
its value. 

In doing this, it is unnecessary to bring the decimals into roods 
and perches, or to retain more of them than the three next the 
acres ; as the operation is thus considerably simplified. 

If the fourth figure in the decimals be 5, or greater, add 1 to 
the third : that is, if the content be 3.54585, set down 3.54>6. 

When the content does not amount to an acre, and the number 
of decimals is under five, add as many ciphers to the left, as will 
complete that number : that is, if the content be .8626, set down 
.086. Then, multiply the acres and decimals, contained in each 
number, by the valuation per acre, put upon the respective num- 
bers, and the product will be the value in shillings and decimals. 

MISCELLANEOUS OBSERVATIONS ON VALUING 

LAND. 

1 . Proprietors ought to be very judicious in appointing com- 
missioners, to value for an inclosure. They should not only be 
well acquainted with the quality of the soil ; but should also be 

x2 



308 LAND-SURVEYING. (Part VI. 

able to judge how far every part of the Common is capable of 
being improved, after it has been inclosed, or they will not be 
able to put a just valuation upon it. 

2. In valuing, not only the quality of the land, but also its 
situation, must be attended to ; for, if one part of the land to be 
divided, lies in a valley, (not subject to be flooded.) near a pro- 
prietor's messuage, and another part upon a hill, at the distance 
of two or three miles : it is evident, allowing the land to be all 
of the same quality, that the former situation is much more de- 
sirable than the latter : because it is nearer the house-stead, and 
consequently better situated for receiving agricultural improve- 
ments. 

3. The manner in which the climate and seasons may operate 
upon the produce of the ground, in consequence of its local 
situation, should always be taken into consideration. If one 
field lies towards the south, and another towards the north, and 
both be of the same quality ; the field that faces the south is 
more valuable than the other, as the crops on the former will 
not only be brought to a greater degree of perfection by the 
benign influence of the sum, but will also be ready for the sithe 
or sickle much sooner ; and consequently may be brought to an 
earlier, and frequently to a better market. 

4. In valuing a Common for an inclosure, the improvements 
that may be made by fencing, draining, and cultivation, should 
never be overlooked. If one person should have an allotment 
awarded to him in the best part of the Common, but where no 
improvement can be made ; and another person's allotment, of 
equal value, be laid out in the worst part of the Common, but 
where much improvement may easily be made by cultivation, 
it is manifest that the latter allotment will, in a few years, be 
more valuable than the former. Besides, as quantity is always 
given to compensate for any deficiency in quality, the proprietor 
who has his common-right laid out in the worst part of the 
ground, will not only receive more land than the other : but 
will soon be able, by a trifling expense in cultivation, to make 
it worth more per acre. 

5. In valuing either old inclosed lands or commons, the dis- 
tance of the ground from good springs of water should be re- 



Section II.) land-surveying. 309 

garded. In many parts of England, and particularly upon the 
Wolds in Yorkshire, the occupiers of land frequently suffer 
great inconvenience in driving their cattle a considerable dis- 
tance to watering -places ; and the cattle themselves are some- 
times much injured, in droughty summers, for -want of a re- 
gular supply of wholesome water. Hence a farm that is well 
watered is worth more to rent, than another farm of equal 
quantity and quality, but destitute of water. 

0. The distance of farms, common-rights, &c. from market- 
towns is also of considerable importance ; because land always 
increases in value as it approaches the vicinity of large towns. 
Besides, as tillage abounds in such places, the means of im- 
provement may be obtained at a much less expense, for ground 
situated in the environs of towns, than for that which lies at 
the distance of several miles. It may also be remarked, that 
the occupiers of the former can always find a ready market for 
the produce of their land, while the occupiers of the latter are 
under the necessity of being at a considerable expense in trans- 
porting their goods to market; and in procuring the various 
articles that are indispensably necessary for the use of their 
families. 

Note. — Here It may not be improper to explain to the young Surveyor, a 
few of those terms by which commons and uninclosed lands are usually de. 
nominated. 

Appellations given to Commons. 

1 . Moors are large, uncultivated tracts of ground, generally 
overgrown with furze, broom, heath, and other small shrubs, 
as Rumbles-moor in Yorkshire, and Blackstone-edge, partly in 
Yorkshire, and partly in Lancashire. 

2. A Fell is a large, open portion of land, generally less 
overrun with shrubs than a moor, as Gateshead Fell in the 
county of Durham. 

3. A Heath is any open ground, abounding with the plant 
called heath, or any other shrubs, as Hounslow Heath in Mid- 
dlesex. 

4. "Wolds are high, open grounds, as the Wolds in York- 
shire and Lincolnshire. 

x3 



310 land-surveying. (Part VI. 

5. Downs are fine, open, pasture grounds, as the Downs in 

Kent, Sussex, and Surrey. 

6. Fens are low, wet, tracts of ground, as the Fens in Lin- 
colnshire. 

7. Marshes are low, swampy grounds ; and when adjoining 
the sea, or the sides of rivers, they are mostly excellent pastures ; 
as the Marshes in the counties of Durham and York, contiguous 
to the river Tees : those in the counties of York and Lincoln, 
contiguous to the river Humber ; and the rich marsh of Romney, 
in the county of Kent, adjoining the straits of Dover. 

8. Mosses are black, turfy, boggy moors, as Ashton Moss, 
and many others in Lancashire. 

9. Forests are wild, uncultivated tracts of ground, generally 
abounding with trees, as Sherwood Forest, in Nottinghamshire, 
and the New Forest, and that of East Bere, in Hampshire. 

10. Ings are large, open meadows, generally situated on low, 
level grounds. Fields and tracts of land known by the local 
name of u The Ings," abound in almost every county of Eng- 
land. 

11. Holmes are hilly, fenny, or level grounds, adjoining to, 
or encompassed by rivulets or brooks. Many rich and fertile 
pasture grounds, in this country, are known under the local 
appellation of i; The Holmes." 

12. Ope>*-fields are uninclosed lands, generally divided into 
furlongs, by mereforms ; and occupied by different tenants. 

Some furlongs are usually in corn, some in meadow, and 
others in pasture ; and the cattle and sheep which depasture, 
are tended by shepherds. Large tracts of land upon the 
Wolds, in Y'orkshire, are cultivated in this manner. 

13. A Furlong of land is used, in some old books, to express 
the eighth part of an acre ; hence 20 perches or 605 square 
yards, make a furlong. 

The term is also used to denote anv number of lands ad- 



Section II.) LAND-SURVEYING. 311 

joining each other, in open fields, and running in the same di- 
rection from one head-land to another; and known by some 
particular name, in order to distinguish the different parts of 
the field from each other. 

14. Mereforms are narrow pieces of swarth, dividing lands, 
or furlongs, in open-fields, from each other. 

15. An Ox-gang, or Ax-gate of land is usually taken for 15 
acres ; being as much land as it is supposed one ox can plough 
in a year. 

In Scotland, 13 acres are denominated an Ox-gang ; and in 
some places, the term is used to denote as much land as will 
summer one ox. 

This word is corruptly called Osken in Lincolnshire, and 
some other counties. 

16. A Hide of land, sometimes met with in old books, was 
such a quantity as might be cultivated, in the compass of a year, 
with one plough ; having meadow and pasture sufficient to feed 
the cattle belonging thereto. The term was also frequently 
used to denote as much land as would maintain a family. 

Some writers make the hide to contain 60, some 80, some 
100, and others 120 acres. 

Sir William Dugdale, the antiquarian, says that a Barony, in 
former ages, was a certain portion of land held immediately of 
the king, and contained not less than 40 hides, or 3840 acres ; 
a statement that gives 96 acres to a hide. 



Directions for setting out new Roads, Sand- Pits, Quarries, Water- 
ing-Places, §c. fyc. ; and for dividing Commons and Waste 
Lands into Allotments. 

1. Before commons and waste lands are divided and allotted, 
new roads must be set out upon them, in the most convenient 
and advantageous manner. They should, whenever it is prac- 
ticable, be set out in such directions as to form right-angles, or 
as nearly right-angles as possible, as the places where they meet or 

x4 



312 land-surveying. (Part VI. 

intersect each other, or come in contact with ancient highways. 
They should not be less than thirty feet in breadth; and set 
out in right-lines ; because straight roads not only look better 
than crooked ones, but also occupy less ground. 

2. All old roads leading over commons or waste lands about 
to be inclosed, may be stopped or diverted, at the discretion of 
the commissioners ; and such old roads must be surveyed and 
allotted as part of the commons or waste lands. 

3. Certain portions of commons should always be set out for 
sand or gravel -pits, and for quarries ; if the commons contain 
either sand, gravel, or stone. The portions of ground thus set 
out are considered as public property, from which every person 
who receives a common-right, may take materials for building 
houses, making fences, and repairing roads. 

4. If there be any good springs of water on commons, they 
must either be left uninclosed, for public watering-places ; or 
the water must be conveyed to more convenient situations, by 
means of drains or channels ; and troughs or reservoirs made 
for its reception. 

5. In some places the lord of the manor claims one-twelfth, in 
some one sixteenth, in others only one-twentieth, of all commons 
and waste lands ; whatever be his claim, however, it must be set 
out before any other allotment, after its value has been ascer- 
tained from the quantity and value of the whole common. Be- 
sides this allotment, the lord of the manor, will, of course, be 
entitled to his proportional share of the remainder of the waste 
lands, in the same manner as any other proprietor. 

6. When it .can be done, it is very desirable to ascertain the 
value of all the tythes, and to set out, for the proprietor of the 
tythes, an allotment of equivalent value ; thus will the whole 
place become tythe-free ; and the occupiers of lands be exempt 
from what they generally deem an unpleasant tax upon their 
industry ; but which is, nevertheless, as justly due to the pro- 
prietor of the tythes, as the rent of a farm is to the landlord. 

7. If the clerk's salary arise from the lands, Avhich is the case 



Section II.) land-surveying. 318 

in some places, a common-right may also be set out in lieu of it ; 
and if another can be obtained as a small endowment for a 
town's school, the inhabitants will not have cause to repent, if 
they be judicious in the choice of a master. 

8. After the roads, sand-pits, quarries, watering-places, mano- 
rial right, &c. &c. have been set out, the remainder of the com- 
mon or waste lands must be equitably divided, (quantity, qua- 
lity, and situation of place being regarded,) among the owners 
and proprietors of messuages, cottages, lands, tenements, and 
hereditaments situated in the township or place where the in- 
closure is to be made and executed. 

Note 1 . — The first step towards inclosing wet, marshy grounds, is to have 
them well drained ; for without this be done, every attempt at improvement 
will be vain. Mr. Elkington's method of draining land, drawn up by Mr. 
Johnstone, (price twelve shillings in boards,) and published under the direction 
of the Board of Agriculture, has eclipsed every other work on this subject. 

See my Treatise on Practical Mensuration, Part V I ., for a particular account 
of Mr. Elkington's manner of draining ; for the great agricultural improve- 
ments lately made in the counties of York and Lincoln, by means of exten- 
sive drainages ; and for the method of measuring hay-stacks, drains, canals, 
marl-pits, ponds, mill-dams, embankments, cpuarries, and coal-heaps. 

2. — As Land-Surveyors are frequently employed to measure and value 
standing-timber, in gentlemen's estates, I beg leave to refer them to my 
Mensuration, Part IV., where I hope they will find these subjects satisfac- 
torily treated. 

The work also contains the Mensuration of Superficies and Solids in 
general ; the method of measuring Artificers' Works ; Conic Sections and 
their Solids ; and the most useful Problems in Gauging. 



To determine the Value of each Proprietors Allotment, or claim 
upon the Common. 

In doing this, the value only can be used ; for, if we make 
use of the quantity, in allotting land of different qualities, the 
proprietor who has his allotment in land of the best quality, will 
obviously receive more than his just right ; while those, whose 
allotments fall in land of inferior quality, lose part of their pro- 



s 

14 LAND-SURVEYING. (Part VI. 

perty. Hence, you must say, as the value of the whole estates, 
is to the value of the Common, or land to be divided, so is the 
value of each person's estate to the value of his allotment, or 
claim upon the Common. 



To set off\ upon the Plan, each Proprietor's Allotment, or Share 
of the Common. 

When you find that a proprietor's allotment falls in that part 
of the Common, which is of uniform quality, you may easily 
determine the quantity to which he is entitled, by saying, as the 
value put upon the number in which his allotment falls, is to 1 
acre, so is the value of his claim, to the quantity of land which 
his allotment must contain. Then set off the allotment upon 
the plan, by some of the methods already described. 

But it commonly happens that a proprietor's allotment falls in 
different numbers. In such a case, you must draw a guess-line, 
or lines, and measure separately, by the scale, the pieces cut off 
belonging to the different numbers : then multiply the different 
quantities by their respective values, and if the sum of the pro- 
duets be equal to the value of the claim in question, the guess- 
line or lines, are right ; if not, they must be altered, until they 
part off the exact portion. After each proprietor's allotment is 
set off upon the plan, if you find the quantity and value of all 
the allotments equal to the quantity and value of the whole 
Common, the division is right. 



EXAMPLE. 

Lay down a Plan from the engraven Field-Book, belonging 
to Plate XII. ; and divide the Common among the three Pro- 
prietors, A, B, and C, according to the different qualities of 
their Estates, and of the Common. 



Section II.) land-surveying 



315 



A Book of Quantities, Qualities, Values, #e. 



Belonging to Plate XII. 



No. 

on the 
Plan. 


A's Estate. 


Quantity. 
~V7DecT 


Qua- 
lity. 


Value. 
Shil. Dec. 


1 

2 

3 

Total 


7.565 
7.609 
7.301 


x s 

X 

xh 


378.250 
304.360 
277.438 


22.475 




960.048 


4 
5 
6 

"Total 


B's Estate. 


7.858 
7.892 
8.223 


X c 
X o 


290.746 
260.436 
328.920 

~~ 8807f02~" 


23.973 


Tf 
1 

8 
9 

Total 


C's Estate. 


7.819 
7.078 
7.481 


xh 
X so 
X s 


297.122 
424.680 
374.050 


22.378 




1095.852 


10 
11 
12 
13 

Total 


The value 
whole Esl 


ofthe 
ates. 


2936.002 


The Common. 


10.061 

4.680 

4.446 

5.995 

"25.182 


X 

xd 
xh 
sh 


301.830 
159.120 
168.948 
167.860 


797.758 



Note 1.— The learner should lay down the plan, from the field-notes, by 
a scale of two chains to an inch ; and find the areas of all the fields from his 
own dimensions, as directed in Part V. The diagonals and perpendiculars 
from which the above areas were found, are not given, as this would have 
rendered the work too easy to exercise the genius of the student ; he may, 
however, retain his own dimensions, and enter them in " a Book of Dimen- 
sions, Castings, Quantities, Qualities, and Values, adapted to Plate XII." 
(See the Bool s of Dimensions and Castings, in Part V., belonging to Plates 
VIII. and X.) 



316 land-surveying. (Part VI. 

2. — If the learner should not be able to find such dimensions as will make 
his areas agree exactly with those given in the foregoing book of quantities, 
it will be a matter of no consequence, provided the difference be not too 
considerable ; and as any difference in the areas will also produce a dif- 
ference in the values, all the numbers in his book will differ from the given 
numbers. This, however, will tend much to his improvement, as he will be 
under the necessity of making all his own calculations, both in finding the 
areas and- values of the different fields, and also in dividing the Common, 
and proving the Division. 



The Operation of finding the Value of each Proprietors Share of 
the Common ; and Directions for setting out the Allotments in 
the Field. 

s s 

s. s. ( 960.048 ) ( 260.860 ) A's ) 

As 2936 : 797.758 :: - 880.102 V : \ 239.137 >B's value. 
1095.852 j ( 297.761 ) C's j 
797.758 proof. 



As the whole of A's allotment will fall in No 10, we say, as 
30 : 1 :: 260.860 : 8.695 acres, the quantity of land which 
A's allotment must contain. 

From 10.061 take 8.695, and we have 1.366, the remainder 
of No. 10, in value = 40.980, which will form part of B's allot- 
ment. Then, from 239.137, take 40.980, and there remains 
198.157; consequently, B must have land equivalent to this 
value, from Nos. 11 and 12. 

The remainder of these Nos. and the whole of No. 13, will 
be C's allotment, which you must measure, &c. as a proof. 

In setting off the allotments upon the plan, we find that one 
end of the division-fence between the allotments of A and B, 
falls at the distance of 827 links from + 8 toAvard -J- 1 ; and 
the other end at the same distance from -f- 7 toward -j- 2. We 
find, likewise, that one end of the division-fence between the 
allotments of B and C, falls at the distance of 1465 links from 
-f 8 toward -j- 1 ; and the other end at the distance of 1478 



Mrf/rXi 



jL ^ /^ <fe. 



^ 




I ^(Uy/^^^u^ra^miicl^iooL^ dc/sd. 



h 






- 


°1 


>■ — / 


,v 


1 

3?J 


5 


JO 




4 


.r r 


6 




11 12 


■>.') 


.^v/ \ .••/ ' 




7 

>— 


8 


9 

._/•./ 




13 


j, 



- 5 fe J /, //, / / //,////■ i //' •/// Z///70. 



Section II.) LAND-SURVEYING. 317 

links from + 7 toward -f 2. Measure, therefore, these dis- 
tances in the field, stake out the division-fences, and the work 
will be completed. 

Note. — The fences of old inclosures are generally very crooked ; but the 
fences of new inclosures are always set out in straight lines, when it is prac- 
ticable. 



THE PROOF OF THE DIVISION. 



No. on the 
Plan. 


A's Allotment. 


Quantity. 
A. Dec. 


Quantity. 
A. R. P. 


Qua- 
lity. 


Value. 
Shil. Dec. 


Part of 10 


8.695 


8 2 31 1 


X i 


260.850 


Part of 10 
11 


B's Allotment. 


1.366 
2.580 
2.910 




X 
X d 

TT h 


40.980 

87.720 

110.580 




1° 






I ■"■ " 


Total 


6.856 


I 6 3 16 | 


239.280 


Part of 11 
12 


C's Allotment. 


2.100 
1.536 
5.995 




X d 
X h 

s h 


71.400 

58.368 

167.860 




Whole of 13 






Total 


9.631 


9 2 22 




297.628 


1 Sum total 


25.182 


25 29 


797.758 



Note 1. — In dividing land by this irregular method, (the only one practica- 
ble, when an allotment falls in land of different qualities,) it is almost impos- 
sible to get the quantity and value of all the allotments to agree exactly with 
the quantity and value of the whole Common ; but when the difference is 
trifling, we may rely upon the accuracy of the division. 

2. — All the fences of the estate in Plate XII. are made straight, in order 
to avoid trouble in casting the contents ; and as the allotments are small, 
neither roads, sand-pits, quarries, nor watering-places, are set out ; but as 
copious directions have been given on these and other subjects, the Author is 
persuaded that if these directions be well understood, the learner will find 
no difficulty in performing any operation that may be wanted in conducting 
an extensive inclosure, so far as appertains to the business of a Land-Sur- 
veyor. 



ais 



LAND-SURVEYING. (Part VI. 



9rt* of parliament 

FOR INCLOSING COMMONS AND WASTE LANDS. 

All commons and waste lands are inclosed under Special Acts of Parlia- 
ment obtained for that purpose ; and the Commissioners and Surveyors are 
always appointed by name, in such Acts. 

The preamble of a Special Act, sets forth the manor, township, parish, 
and county in which the commons or waste lands are situated ; specifies the 
names of such commons and waste lands, and the quantity of ground they 
contain, either by survey or estimation ; notices the little profit and ad- 
vantage they afford in their present state ; and points out the improve- 
ments they are capable of receiving, if they be divided, allotted, and inclosed. 

In order to diminish the expense attending the passing of Special Acts of 
Inclosure, for particular places, a General Act was passed in the year one 
thousand eight hundred and one, consolidating and containing certain pro- 
visions usually inserted in Special Acts of Inclosure. 

This Aet is made the foundation of all Special Acts, and contains the 
same provisions, with the exception of particular clauses that are always 
inserted in Special Acts of Inclosure, relating to, and making provision for, 
local circumstances. 

Now, in order that no necessary instructions may be wanting m this 
Work, relating to Inclosures, it has been thought advisable to give an ab- 
stract of the General Inclosure Act, for the information of those readers 
who may not have an opportunity of consulting the Aet itself. 

It will be found from this statute, that no person can act as a Commis- 
sioner, until he has first taken an oath that he will faithfully, impartially, 
and honestly, according to the best of his skill and ability, execute and 
perform all the trusts, powers, and authorities vested and reposed in him, 
as a Commissioner. 

It also appears by this Act that every person making a survey, plan, 
and valuation for an inclo. r : ..:. -.., shall verify the same upon oath, to the 
Commissioners. 

The Act likewise points out the method of ascertaining the boundaries of 
manors or lordships ; making out claims ; settling disputes ; setting out 
roads ; fencing allotments ; defraying the expenses of the inclosure, &c. &c. 

Besides giving an abstract of the General Act, a few particular clauses are 
selected from Special Acts, obtained for inclosing certain commons and 
waste lands in the West Riding of the County of York. 



Section II.) LAND-SURVEYING. 319 



GENERAL ACT. 

An Abstract of an Act for consolidating in one Act, certain 
Pi*ovisions usually inserted in Acts of Inclosure ; and for 
facilitating the Mode of proving the several Facts usually 
required on the passing of such Acts. (July 2nd, 1801.) 

Whereas, in order to diminish the expense attending the passing of Acts 
of Inclosure, it is expedient that clauses usually contained in such Acts 
should be comprised in one law, and certain regulations adopted for facili- 
tating the mode of proving the several facts usually required by Parliament, 
on the passing of such Acts : May it, therefore, please your Majesty, that 
jt may be enacted ; and be it enacted by the King's most excellent Majesty, 
by and with the advice and consent of the Lords Spiritual and Temporal, 
and Commons, in this present Parliament assembled, and by the authority 
of the same, that no person shall be capable of acting as a Commissioner in 
the execution of any of the powers to be given by any Act hereafter to be 
passed for dividing, allotting, or inclosing any lands or grounds, except the 
power of signing, and giving notice of the first meeting of the Commissioner 
or Commissioners for executing any such Act, and of administering the oath 
or affirmation hereinafter directed, until he shall have taken and subscribed 
the oath or affirmation following : 

* I, A. B. do swear, (or being one of the people called Quakers, do solemnly 
' affirm), that I will faithfully, impartially, and honestly, according to the 
' best of my skill and ability, execute and perform the several trusts, powers, 
' and authorities vested and reposed in me as a Commissioner, by virtue of 
1 an Act for (here insert the title of the Act), according to equity and good 
' conscience, and without favour or affection, prejudice or partiality, to any 
' person or persons whomsoever. So help me God.' 

Which oath or affirmation it shall be lawful for any one of the Commis- 
sioners, where more than one shall be appointed by any such Aet, or any 
one Justice of the Peace for the County within which the said lands or 
grounds shall be situated, where only one Commissioner shall be so ap- 
pointed, to administer, and the said oath and also the appointment of every 
new Commissioner, shall be enrolled with the award, and a copy of the 
enrollment admitted as evidence. 

2. Commissioners declining to act, shall give notice, in writing, of such 
intention, to the other Commissioners ; and no Commissioner shall be ca- 
pable of purchasing any lands within any parish in which the inclosures are 
to be made, until five years after the date and execution of the award to be 
made by any such Commissioner, or Commissioners. 



320 land-surveying. (Part VI. 

3. And whereas disputes may arise concerning the boundaries of parishes, 
manors, hamlets, or districts, to be divided and inclosed, and of others ad- 
joining thereto, Commissioners shall inquire into the boundaries of parishes, 
and if not sufficiently ascertained, they shall fix them, giving previous notice 
of their intention so to do. 

The Commissioners shall cause a description of boundaries to be delivered 
to one of the Church- Wardens, or Overseers of the poor of the respective 
parishes, and to the Lords of Manors or their stewards ; and if any such 
person or persons be dissatisfied with the determination respecting the said 
boundaries, they may appeal to the quarter-sessions, the decision of which 
is to be final. 

4. A true, exact, and particular survey, admeasurement, plan, and valua- 
tion of all the lands and grounds to be divided, allotted, and inclosed by any 
such Act ; and also of all the messuages, cottages, orchards, gardens, home- 
steads, ancient inclosed lands and grounds within any such parish or manor, 
shall be made, and kept by the Commissioners ; and the same shall be veri- 
fied upon oath or affirmation by the person making such survey, valuation, 
&c. at any meeting to be held after the making hereof. 

Proprietors, and their agents, may inspect admeasurements and plans, 
and take copies or extracts therefrom. 

5. Until the division shall be completed, the lands may be entered by the 
Commissioners, or any persons they may appoint to make surveys, valua- 
tions, &c. &c. 

Maps made at the time of passing Acts, may be used, without making 
new ones, if the Commissioners shall think fit. 

6. All persons who shall have or claim any common or other right to or 
in any such lands to be inclosed, shall deliver to the Commissioners schedules 
of particulars, or shall be excluded ; and such claims may be inspected, 
and copies taken. 

Objections to claims to be delivered to the Commissioners at or before 
the meeting appointed for that purpose, or they shall not be received, ex- 
cept for special causes 

7. Commissioners are not hereby authorised to determine disputes touch- 
ing rights ; but they shall assign the allotments to the persons in actual 
possession of the land. 

8. Commissioners before making any allotments are to set out and appoint 
the public carriage-roads and high- way s through and over the lands and grounds 
intended to be divided, allotted, and inclosed ; and to divert, turn, and stop up 



Section 1 1. J land-surveying. 321 

any of the roads and tracts upon any part of the said lands, as they shall 
judge necessary, so as such roads and highways shall be and remain thirty 
feet wide at the least, and the same shall be set out in such directions as shall 
appear to them most commodious to the public. They shall also ascertain 
the same by marks and bounds ; and prepare a map thereof to be deposited 
with their Clerk, and give notice thereof, and appoint a meeting, at which, 
if any person shall object, the Commissioners with a Justice of the Division 
shall determine the matter. 

If the Commissioners by any Bill shall be empowered to stop up any old 
road, it shall not be done without the order of two Justices, which order 
shall be subject to appeal to the Quarter Sessions. 

9. The carriage-roads shall be well fenced on both sides, by such of the 
land-owners as the Commissioners shall direct ; and no person shall erect 
any gate across any road, or plant any trees on the sides, at less than fifty 
yards distance. 

The Commissioners shall appoint Surveyors of the roads, and if with a 
salary, such salary, and the expense of making the road, over and above 
the statute duty, shall be raised in the same manner as the charges and ex- 
penses of obtaining and passing any such Act ; and shall be directed to be 
raised and paid to such Surveyors on or before the execution of the award. 

Surveyors of roads are directed to be in all respects subject to the controul 
of the Justices of the Peace, acting in and for the county in which such roads 
shall respectively lie ; and shall account to such Justices for all monies re- 
ceived and expended ; and for the re-payment of any surplus which may 
remain in their hands, to such persons as shall have been made liable to con- 
tribute thereto, according to the proportion so as above ascertained by such 
Commissioners ; and such Justices shall have the power of levying any such 
rates as may be thought necessary for the purpose aforesaid, according to 
the proportions previously ascertained by the Commissioners. 

If Surveyors neglect to complete roads within a limited time, they shall 
forfeit £20, and the inhabitants shall not be charged or chargeable towards 
forming or repairing the said roads, (except statute duty,) till such time as 
the same shall be declared to be completed, at a Special Sessions. 

10. Commissioners are empowered and required to set out and appoint 
such private roads, bridleways, footways, ditches, drains, watercourses, 
watering-places, quarries, bridges, gates, stiles, mounds, fences, banks, 
bounds, and land-marks, in, over, upon, and through or by the sides of the al- 
lotments to be made, as they shall think requisite, giving such notice, and sub- 
ject to such examination as may be required. And the same shall be made 
and at all times kept in repair, by the owners and proprietors, for the time 
being, of the lands and grounds directed to be divided and inclosed, in such 
proportion as the Commissioners shall, by their award, order and direct. 

Y 



322 land-surveying. (Part VI. 

II. The grass and herbage on roads shall belong to the proprietors of the 
lands adjoining on either side ; and all roads which shall not be set out as 
aforesaid, shall be stopped op, and be deemed and taken as part of the 
lands and grounds to be inclosed ; and shall be drvid :. and in- 

closed accordingly. 

-mpike-road shall be altered or diverted, without the consent of the 
trustees of such turnpike-road. 

12. Commissioners, in making the several allotments, shall have due re- 
gard as well to the situation of the respective houses or homesteads of 
proprietc : - if the lands and grounds to be 
allotted to them respective Iy, bo fin - be consistent with the general 
convenience of the said proprietors ; and the Commissioners, in making the 
said allotments, choJI have par:. ,-^rd to the convenience of the 
owners or proprietors of the smalles: m the lands and grounds 
directed to be allotted and exchanged. 

13. And whereas the proprietors and persons interested in open common- 
fields, meadows, pastures, commons, and waste lands, directed to be divided 
and allotted, whose allotments thereof will be small, and expensive to in- 
close, may he desirous of stocking and depasturing their allotments in com- 
mon, and of sharing such produce as may grow thereon, under proper 
regulations ; therefore the Commissioners shall be fully authorised and 
empowered, on application of the parties interested, at their : :ond 
meeting for receiving claims, and on an attentive view and full consideration 
of the prrii. ises, to a ~ ard, order, and direct any such allotments to be laid 
together, and ring-fenced, and to be stocked and depastured in common, 
and to make such orders and regulations for the equitable enjoyment 
thereof, and for the participation of any produce growing or to grow 
thereon, as the Co m missioners may think beneficial and proper for the 
said several parties Interested therein. 

14. The several shares of and in any lands or grounds which shall, upon 
any such division, be assigned, set out, allotted, and applied unto and for the 
several persons who shall be entitled to the same, shall, when so allotted, be 
and be taken in full compensation for all rights in the lane:- rights 
of commons, and ail other rights and properties whatsoever, which they 
respectively had, and were entitled to, in and over the said lands and 
grounds ; which rights shall cease on notice from the Co mmis sioners being 
affixed on the doors of the parish church ; in which the said lands and 
grounds shall be situated. 

15. Commissioners shall, and they are hereby authorised, to set out, allot, 
and award any messuages, buildings, lands, tenements, hereditaments, new 
allotments, or old inclosures, within such parish or manors, in lieu of or in 






Section II) LAND-SURVEYING. 323 

exchange for any othermessuages,buildings,lands,tenements,hereditaments, 
new allotments, or old inclosures, within the said parish or manors, or within 
any adjoining parish or place ; so that all such exchanges be made with the 
consent of the respective owners and proprietors, seized of the lands, &c, 
which shall respectively be so exchanged : or if belonging to or held in right 
of any church, chapel, or ecclesiastical benefice, shall also be made with the 
like consent, in writing, of the bishop, the patron, &c. for the time being ; 
and all such exchanges shall be for ever good, valid, and effectual in the 
law, to all intents and purposes whatsoever. 

16. Commissioners may make allotments in severalty to joint tenants, or 
tenants in common ; and immediately after the said allotments shall be made 
and declared, the same shall be holden and enjoyed by the person or persons 
to whom the same shall be allotted in severalty, in the same manner, and 
subject to the same uses, as the undivided part or shares of such estates 
would have been held in case such partition and division had not been made. 

17. All persons to whom any allotments shall be made, are required to 
accept of their respective allotments within the space of two calendar 
months next after the execution of the award, directed to be made, and in 
case any persons shall neglect or refuse to accept of their share or allot- 
ment within the time before-mentioned, such persons so neglecting or re- 
fusing shall be totally excluded from having or receiving any estate or 
interest, or right of common whatsoever, in any part of the lands and 
grounds to be divided and inclosed. 

18. It shall and may be lawful for the respective guardians, husbands, 
trustees, committees, or attorneys, of any persons being minors, femes 
covert, lunatics, beyond the seas, or otherwise incapable by law, to accept any 
such allotments as shall be made by any such act, to and for the use of such 
persons so incapacitated as aforesaid ; and also that any persons entitled to 
any allotments as tenants for lives, shall be, and are hereby respectively 
enabled and required to accept of and take such allotments. 

The non-acceptance of any guardians, husbands, &c. &c, shall not ex- 
clude, or in any way prejudice the right of any person, incapacitated as 
aforesaid, who shall claim or accept such share or allotment within twelve 
calendar months next after such incapacity shall be removed. 

19. After the allotments shall be set out by such Commissioners, and at 
any time before the execution of their award, it shall be lawful for any per- 
sons to whom any allotments shall be so made, and staked, and marked out, 
by and with the consent of such Commissioners, in writing under their 
hands, to ditch, fence off, and inclose their respective allotments, in such 
manner as such Commissioners shall so direct and appoint. 

Y 2 



324 land-surveying. (Part VI. 

20. The timber trees and other trees, thorns, and bushes, standing and 
growing upon any waste lands, or other lands to be allotted by such act, 
shall be allotted and go along with the lands whereon they respectively stand, 
and shall be deemed the property of the several persons to whom the same 
lands shall be respectively allotted, such persons paying to the owner or 
respective owners of the said trees, such sums of money for the same, and 
at such times, and places, as the said Commissioners shall, by writing under 
their hands, direct ; but if the said parties, who are to make such respective 
payments, shall neglect or refuse to make the same accordingly, then it shall 
be lawful to and for the respective parties who shall be entitled to have and 
receive such payments, to enter on the said lands, and cut down, take, and 
carry away to their own use, the said trees, thorns, or bushes, in respect of 
which the said payments were respectively to be made to them, at any sea- 
sonable time, within one year next after such neglect or default, they doing 
as little damage on the said lands as may be. 

21. Whenever any sum of money is, under the provision of this Act, or 
any such Bill, to be paid for the purchase or exchange of any lands, tene- 
ments, or hereditaments, or of any timber or wood growing thereon, and 
which sum of money ought to be laid out in other purchases, to be settled 
to the same uses, it shall and may be lawful for the Commissioners, out of 
such sum, to defray such proportion of the expense of passing such Act, 
and of carrying the same into execution, as shall, if any, be charged upon 
any of the lands, tenements, or hereditaments so sold or exchanged. And 
if the surplus money shall amount to the sum of £200, it shall, as soon as 
convenient, be laid out in other purchases, and in the mean time, until 
such purchase can be made, such money shall be paid into the Bank of 
England, in the name and with the privity of the Accountant General of 
the High Court of Chancery, to be placed to his account there. And such 
money shall be applied under the direction, and with the approbation of the 
Court of Chancery. 

22. If such money be less than £200, and shall exceed the sum of £20, it 
shall, at the option of the persons entitled to the rents and profits of the 
lands, be paid into the Bank, as aforesaid, in order to be applied in the man- 
ner before directed ; or otherwise the same shall be paid at the like option, 
to two trustees to be named by the person making such option, and to be 
approved of by the Commissioners, (such nomination and approbation to be 
signified in writing under the hands of the nominating and approving 
parties,) in order that the money be applied as before directed. 

23. Where such money shall be less than £20, it shall be applied to the 
use of the persons who would for the time being have been entitled to the 
rents and profits of the lands, in such manner as the Commissioners shall 
think proper. 



Section II.) land-surveying. 325 

24. If any persons to whom any allotments shall be made, do not accept, 
inclose, and fence their allotments as the Commissioners 'shall direct, they 
may cause such allotments to be inclosed and fenced, and let the same to any 
persons they may think proper ; and they may receive the rents and profits 
thereof, until the expenses attending the inclosure and fencing thereof are 
paid ; or they may charge such expenses npon the proprietors of the allot- 
ments, by any such writing as aforesaid, or by their award, appoint to 
whom, and at what times the same shall be paid. 

25. It shall be lawful for the several proprietors of the allotments to be 
made in pursuance of any such Aet, their agents or workmen, at any sea- 
sonable times, within the space of seven years next after the fencing of any 
allotments, to set up and erect posts and rails, or other dead fences, on the 
outside of the ditches bounding their respective allotments, not exceeding 
three feet from such ditches, for the preservation of their quickset-hedges ; 
and at any seasonable tunes, before the expiration of the said term, to take 
and carry away the materials of such outside fences, when they shall think 
prober. 

26. No fences or hedges standing when any act is passed, shall be cut 
down or destroyed by the owners thereof, until the execution of the award, 
without the consent of the Commissioners ; and if assigned by them as a 
boundary or division-fence to and for any of the allotments, all such fences 
or hedges shall be left uncut, for the benefit of the persons to whom such 
allotments shall belong ; and they shall make such compensation to the 
former owners thereof, as the Commissioners shall, by writing under their 
hands, hi that behalf order and appoint, 

27. No proprietor whose allotments or shares shall, upon any such inclo- 
sure, lie and be situated next and adjoining to any common-fields, or inclosed 
grounds, the boundary of which shall be fenced by any mound, fence, brook, 
or rivulet, shall be compelled to make or erect any hedges, ditches, or fences, 
next adjoining to any such common-fields, or inclosed grounds, for inclosing 
such their allotments or shares ; but that the whole mound, fence, brook, or 
rivulet, or other sufficient fences which divide any such common-fields, or in- 
closed grounds from such allotments, shall for ever be and remain a boundary 
fence for the purpose of such division : and shall from time to time be main- 
tained, kept, cleansed, scoured, and repaired by the respective proprietors 
thereof, in the same manner as the Commissioners shall order and direct. 

In case it shall happen that some of the proprietors shall have a greater 
proportion of fences to make and maintain upon any of the lands directed to 
be divided and inclosed, than, in the judgment of the Commissioners, they 
ought to be charged with, it shall be lawful for the Commissioners, where they 
shall judge it proper, to ascertain and appoint such sum of money to be paid to 
every such proprietor, towards making and maintaining such fences, by such 

Yd 



326 LAND-SUE YE V I xg. (Part VI 

other of the proprietors who may have a less proportion of fencing, according 
to the value and quantity of the lands to be allotted to them ; and to grant 
such other relief in respect thereof, out of the money to be raised for de- 
_- the expenses of carrying such Act into execution, as they shall think 
reasonable, in order that the said boundary fences may be brought as near 
as may be to a just and equal proportion. 



28. In case any person shall wilfully and unlawfully break down, destroy, 
carry away, or damage any fence, stile, post, rail, gate, bridge, or tunnel, 
which may be put or placed under the authority of any such Act, every 
person so offending, and being thereof convicted before any Justice of the 
Peace for the County in which the lands or grounds to be inclosed shall be 
situated, on confession or on proof of the offence, by oath of one or more 
credible witnesses, (which oath the said Justice is hereby authorised to ad- 
minister,) shall for every such offence forfeit and pay any sum not exceed- 
ing £5 ; and every person shall be allowed to give evidence of such offence, 
notwithstanding he may be a proprietor or occupier of lands within, or an 
inhabitant of such parish, and notwithstanding he may be the owner of any 
such fence, stile, ice. &c. to be recovered as hereinafter provided. 

29. If it shall be provided by any such Act, that the expenses of obtain- 
ing and carrying the same into execution, shall be paid in proportion, by the 
proprietors of lands or grounds to whom any allotments shall be made ; then 
and in such case, when and so often as any such persons, except those ex- 
empted from payment of any such charges and expenses, shall refuse or 
neglect to pay their proportion of the charges or expenses, or shall refuse 
or neglect to pay the expenses attending the inclosing and fencing of any 
such allotments, as upon the neglect or refusal of the proprietors, shall be 
inclosed and fenced by the Commissioners, as hereinafter mentioned, at the 
respective days and rimes to be appointed for payment of such charges and 
expenses, k shall be lawful for such Commissioners, by any warrants under 
their hands and seals, -directed to any persons whomsoever, to cause the said 
costs, charges, and expenses, and sum or sums of money respectively, to be 
levied by distress and sale of the goods and chattels of the persons so making 
default in payment as aforesaid, their guardians, husbands, trustees, com- 
mittees, or attorneys, wheresoever the same shall be found, rendering the 
overplus (if any) on demand, to the owners of such goods and chattels, the 
reasonable charges of such warrant, distress, and sale, being first deducted, 
together with the interest, after the rate of £5 per centum per annum, to be 
computed on such shares or proportions, from the time the same shall be 
directed to be paid by such Commissioners as aforesaid ; or otherwise it 
shall be lawful for such Commissioners, or any persons authorised by them, 
to enter upon and take possession of the premises so to be allotted to such 
persons refusing or neglecting to pay as aforesaid, and to receive and take 



Section II) land-surveying. 327 

the rents and profits thereof, until thereby, therewith, or otherwise, the shares 
or proportions, and the said costs and charges so ordered and directed by 
such Commissioners to be paid by such persons as aforesaid, and all in- 
terest on such shares or proportions, to be oomputed from the time the 
same shall, by such Commissioners, be directed to be paid as aforesaid ; and 
also all costs, charges, and expenses occasioned by or attending such entry 
upon and perception of the rents and profits of the said premises, shall be 
fully paid and satisfied. 

BO. And in such case as last aforesaid, it shall T3e lawful for the husbands, 
guardians, trustees, committees, or attorneys of any of the owners or proprie- 
tors of such allotments or exchanged lauds, (except the rector or vicar of 
such parish) to charge such allotments or exchanged lands and premises, 
with such sums of money as such Commissioners shall, by their award, or by 
writing under their hands, either before or after the execution of such award, 
adjudge necessary to pay and defray the said respective shares of the^harges 
and expenses incident to and attending the obtaining such Act, and carrying 
the same into execution, and of charging the said lands as -aforesaid, so that 
the same shall not exceed £5 for every acre of such allotments or exchanged 
lands ; and -to grant, mortgage, surrender, lease, or demise, or otherwise sub- 
ject the lands, tenements, and hereditaments so to be charged, unto such per- 
sons who shall advance and lend the same respectively, their executors, ad- 
ministrators, and assigns, for any term or number of years ; or in case any 
person in possession, who shall or may be liable to and charged with a share 
of the expenses as aforesaid, shall choose to advance, pay, and discharge such 
sums of money, then it shall be lawful for the Commissioners, by any deed 
of writing under their hands and seals, to be attested by two or more credible 
witnesses, in like manner to grant, mortgage, surrender, lease, demise, or 
otherwise subject the said lands, tenements, and hereditaments, to such per- 
sons, respectively paying and discharging the same, for any term or number 
of years, to and for the payment of such sums of money so advanced, paid 
and discharged by them, with interest for the same, to commence on the ter- 
mination of their right in the premises ; so that every such grant, mortgage, 
surrender, lease, or demise, be made with a proviso or condition to cease and 
"be void, or with an express trust to be surrendered or re-assigned, when 
such sums of money thereby to be secured, should be fully paid and satisfied ; 
and also with a covenant to pay and keep down the interest, so that no per- 
sons afterwards becoming possessed or entitled to any such lands, &c. shall 
be liable to pay any further or larger arrear of interest than for six calen- 
dar months preceding the time when the title to such possession shall have 
commenced ; and that every such charge, grant, mortgage, &c. shall be 
good, valid, and effectual in the law, for the purpose thereby intended. 

31 . And whereas in such cases as aforesaid, where provision may be made 
in any such Act for charging the expenses of passing such Act, or of executing 

y 4 



328 land-surveying. (Part VI. 

the powers therein contained, or of fencing the respectire allotments, on the 
several proprietors thereof, it may be more convenient for the feoffees or 
trustees of any charity lands or school lands, to have lands deducted from the 
respective allotments, to he made for such charity or school lands, for paying 
the proportionate share in respect of such allotments, of such expenses re- 
spectively, than to raise money on mortgage for those purposes ; therefore, 
it shall be lawful for any such Commissioners, if they shall judge it right 
or expedient, to deduct from the respective allotments to be made to such 
feoffees or trustees, as aforesaid, so much land as shall, in the judgment of 
such Commissioners, be equal in value to their respective proportions of the 
said expenses ; and to allot, assign, and award the same to such persons as 
such Commissioners shall think proper, and who will undertake to pay and 
defray, and shall pay and defray, all such expenses. 

32. In case it shall be provided by any such Act, that the expenses at- 
tending the same shall be paid by sale of any part of the lands so to be in- 
closed, the said Commissioners shall mark and set out such parts of the said 
waste or common lands, as in their opinion, will by sale thereof raise a sum 
of money sufficient to pay and discharge all such charges and expenses, as 
may, by any such Act, be directed to be paid and discharged out of the 
same ; and the Commissioners shall sell such parts of the said lands to any 
persons for the best prices that can be gotten for the same, by private con- 
tract, or by public auctions, to be holden for that purpose, of which six 
weeks' previous notice shall be given. And the persons so purchasing the 
same shall immediately pay (by way of deposit) into the hands of the said 
Commissioners, or such persons as they shall appoint, one-tenth part pf-their 
purchase-money, and pay the remainder thereof within three calendar months 
next after, or at such other time as the said Commissioners shall appoint. 
And in default thereof, the money so deposited, shall be forfeited, and shall 
be applied in carrying such Act into execution ; and the said allotments for 
which the whole of such purchase-money shall not have been so paid, or for 
which there shall be no bidding at such auction, shall be again put up to sale, 
and sold in manner aforesaid, for the best prices that can be gotten for the 
same, or be sold by the said Commissioners, by private contract, for any sums 
not less than the remaining nine-tenths of the prices for which the same were 
respectively sold before, or the amount of one bidding above the sums at which 
the same were respectively put up in the said former auction ; and every allot- 
ment for which the full purchase-money shall be paid,shall immediately there- 
upon be absolutely discharged of andfromall common and other right thereon, 
and be vested in fee simple in, and be inclosed, and thenceforth held in severalty 
by such purchasers thereof respectively,astheirprivate and absolute property ; 
and shall be allotted accordingly, by the said Commissioners ; and the said pur- 
chase-money shall be applied in defraying such charges and expenses as may 
be in any such Act directed to be paid and discharged by the sale of such land. 



Section II.) land-surveying. 329 

33. And, for the better enabling such Commissioners to determine the 
several matters and things, by this or any such Act, referred to their determi- 
nation, it shall be lawful for the said Commissioners, from time to time, as 
they shall see occasion, by any writings under their hands, to summon and 
require any persons to appear before them at any time and place in such 
writing to be appointed, to testify the truth touching the matter in dispute 
between any proprietors or interested persons, or otherwise relating to the 
execution of the powers given by this or any such Act ; and to cause a copy 
of such writing to be served on such persons required to give evidence, or to 
be left at their usual or last place of abode. And all persons so summoned, 
who shall not appear before the said Commissioners pursuant to such sum- 
mons, (without assigning some reasonable excuse for not appearing,) or who 
appearing, shall refuse to be sworn or examined on oath or affirmation, which 
oath or affirmation the said Commissioners are hereby empowered and re- 
quired to administer, (such persons having been paid the reasonable charges 
of their attendance,) and being thereof convicted before one of his Majesty's 
Justices of the Peace of the county or district in which such lands are situated, 
upon information thereof upon oath made before any such Justice, shall for 
every such neglect or refusal, forfeit and pay such sum of money, not ex- 
ceeding £10, nor less than £5, as such Justice shall think fit and order. 

34. Provided always, That no witness summoned to attend such Commis- 
sioners shall be obliged to travel above eight miles from the boundary of the 
parish, manor, or district to be inclosed by any such Act. 

35. And be it further enacted, That as soon as conveniently may be after 
the division and allotment of the said lands and grounds shall be finished, 
pursuant to the purport and directions of this or any such Act, the said Com- 
missioners shall form and draw up, or cause to be formed and drawn up, an 
award in writing, which shall express the quantity of acres, roods, and perches, 
in statute-measure, contained in the said lands and grounds, and the quantity 
of each and every part and parcel thereof which shall be so allotted, assigned, 
or exchanged, and the situations and descriptions of the same respectively ; 
and shall also contain a description of the roads, ways, foot-paths, water- 
courses, watering-places, quarries, bridges, fences, and land-marks, set out 
and appointed by the said Commissioners, as aforesaid ; and all such other 
rules, orders, agreements, regulations, directions, and determinations, as the 
said Commissioners shall think necessary, proper, or beneficial to the parties ; 
which said award shall be fairly ingrossed or written on parchment, and shall 
be read and executed by the Commissioners, in the presence of the proprietors, 
who may attend at a special general meeting called for that purpose, of which 
ten days' notice at least shall be given in some paper to be named in such Act, 
and circulating in the county ; which execution of such award shall be pro- 
claimed the next Sunday in the church of the parish in which such lands shall 



330 LAND-SURVEYING. (Part VI, 

be ; from the time of which proclamation only, and not before, such award 
shall be considered as complete ; and shall, within twelve calendar months 
after the same shall be so signed and sealed, or so soon as conveniently may 
be, be enrolled in one of his Majesty's Courts of Record at Westminster, or 
with the Clerk of the Peace for the county in which such lands shall be situated, 
to the end that recourse maybe had thereto by any persons interested therein, 
for the inspection and perusal whereof no more than one shilling shall be 
paid ; and a copy of the said award, or any part thereof, signed by the proper 
Officer of the Court wherein the same shall be enrolled, or by the Clerk of the 
Peace for such county, or his Deputy, purporting the same to be a true copy, 
shall from time to time be made and delivered by such Officer or Clerk of the 
Peace for the time being, as aforesaid, to any person requesting the same, for 
which no more shall be paid than two-pence for every sheet of seventy -two 
words ; and the said award, and each copy of the same, or of any part thereof 
signed as aforesaid, shall at all times be admitted and allowed in all courts 
whatever, as legal evidence ; and the said award or instrument, and the several 
allotments-, partitions, regulations, agreements, exchanges, orders, directions, 
determinations, and all other matters and things therein mentioned and con- 
tained, shall, to all intents and purposes, be binding and conclusive, except 
where some provision to the contrary is herein or shall be by any such Act 
contained, unto and upon the said proprietors, and all parties and persons con- 
cerned or interested in the same, or in any of the lands, grounds, or premises 
aforesaid ; and also that the said respective Commissioners, if they think it 
necessary, shall form or draw, or cause to be formed and drawn on parch- 
ment or vellum, such maps or plans of the said lands and grounds, the better 
-to describe the several new allotments or divisions to be made, and premises 
that shall be exchanged by virtue of this Act, and which shall express the 
quantity of each allotment in acres, roods, and perches, together with the 
names of the respective proprietors at the time of such division and allotment ; 
winch said maps and plans shall be annexed to and enrolled with the said 
respective award, and shall be deemed and construed in every respect as 
and for part of the said award. 

36. Commissioners shall, and they are hereby recmired to enter in a book 
to be provided for that purpose, a particular account of all sums of money 
received from the proprietors or others during the progress of the inclosure ; 
and also of all the charges, expenses, and disbursements which shall accrue or 
be made by virtue of any such Act, and in carrying the same into execution ; 
which book of accounts shall be kept at the office of their Clerk, open at all 
seasonable times during the progress of the inclosure, and till all the accounts 
are finally settled, for the inspection of any of the proprietors, without fee or 
reward ; and in case any such Commissioners, or their Clerk, shall neglect to 
provide and keep such book of accounts as aforesaid, or refuse the inspection 
thereof to any of the proprietors at seasonable times in manner before men- 



Section II.) land-surveying. 331 

tioned, and shall be convicted thereof, upon the oath of one or more credible 
witnesses, not interested in the intended division and inclosure, before any 
Justice of the Peace of the County in which the lands or grounds to be in- 
closed shall be situate, or of any such other county or place where such Com- 
missioners or Clerk so causing such neglect or refusal, and convicted as afore- 
said, shall forfeit and pay for every such offence any sum not exceeding £1 0, 
nor less than £5, to be levied, recovered, and applied in the same manner as 
other penalties are by this Act directed to be levied, recovered, and applied. 

37. All monies raised under any Act shall from time to time, as often as 
the same shall amount to the sum of £50, be deposited in the hands of some 
banker or such persons as shall be approved by a majority in value of the pro- 
prietors, at the first meeting of the Commissioners, in the notice of which 
meeting shall be expressed the intention of then appointing such banker, or 
such other persons, and no monies deposited or paid into the hands of such 
banker or other persons, to be appointed as aforesaid, shall be issued or paid 
by them, without an order in writing under the hands of such Commissioners, 
specifying the persons to whom the same are respectively payable, and the 
service or consideration for which the same are due ; and the balance, if any, 
upon the final settlement of accounts, shall be immediately repaid to the 
landowners in proportion to the sums respectively paid by them. 

38. It shall be lawful for the rector or vicar of any parish wherein the 
lands and grounds intended to be inclosed shall be situate, by indenture under 
his hand and seal, with the consent of the bishop of the diocese, and of the 
patron of the living, to lease or demise all or any part or parts of the allot- 
ments to be set out and allotted to any such rector or vicar, to any persons 
whomsoever, for any term not exceeding twenty-one years, to commence 
within twelve calendar months next after the executing the award ; so that 
the rents for the same shall be thereby reserved to the rector or vicar for the 
time being, by four equal quarterly payments in every year ; and so that there 
be thereby also reserved and made payable to such rector or vicar, the best 
and most approved rents that can reasonably be gotten for the same, without 
taking any fine, foregift, premium, sum of money, or other consideration for 
the making or granting any such lease or demise ; and so that no such lessee 
by any such lease or demise be made dispunishable for waste, and so that 
there be inserted in every such lease, power of re-entry on non-payment of 
the rents to be thereby reserved, within a reasonable time to be therein 
limited, after the same shall become due ; and so that a counterpart of such 
lease be duly executed by the lessee or lessees to whom such lease shall be 
so made as aforesaid ; and every such lease shall be valid and effectual. 

39. All penalties and forfeitures imposed by virtue of this or any other 
such Act, shall be levied and recovered before any one Justice of the Peace 



I3S : axd-surveyikg. Purl r/. 

for the county in which the lands or grounds to be inclosed shall be sitnate, 



**-'- ~>-::"- : i" :-f i: =".:: .'. " f 7i~-:il : r . r; - 7: 7 .-- : f ■:' :'.: : 7 -:. : ■-. -- -- 
made to him, to sawn die party accused, and the witnesses on 

of the party accused. 
(winch oath any snch Justice is hereby em- 
. - 

ari :•■ :^iriiz 7ir -. ir:;- i::iirl n =~;^- :ii7: ^ 1 = " :' r:' .: _r - ^ -.'--. :'- 
•ri::: siill 11-f z:r:T 7 n 1 :: !f-y - i .7 : fnlr.f- n '. : .::':::_-:- ;- lii- 
1 sale of the offe nd e r ' s goods and chattels, together with reasonable 
: ■:>-; ■ .. " .. _ ---\- ..:.:..-.:. - "... . - ' - 
7_ri. -7. -."_ 5-: si:i i= Tif sin f 7n7 ': t If-lf-i. if :i:: ::r ri 7: i.^f-5 i- 7if 
; shall by writing under their hands or by their award, order 





i-iir rlilf, :r ±:er-r=- ::' ill" l:ri :r 111;- : J n;-ini :r :: l-rdilir;.— riTi.7 f 

are situate; or to the seniorities, rights, and royalties incident or belonging 
to snch manor or lordship, or to the lord or lady thereof. ■ any person 

: :i: :if sin f 7n7 r-fnm. n :. - rill. :r-'.r. n :':-:;■ 

i- 1 jnr-i^fs. :--1t"i::1- :r :i-7:i: ii-f if 11 

=-; f 1 mi r:l:s ':-ff:r-f 7if : .■.■^n: : : ' 5i7i A ::. :r n :ifr :7t Mnf 7_ 1 



4 '_ ?i -vi : ~ - - : 7 . . 

:~*s:r«. ::::: ill "It: ; n- i=. 1:- : :'irl: mi : :rr :riif. n 1 ::fi : : ::-. 
?i::fff ::•;. r-r ■;:::-. i~ 1 i innim: :rs. ill sr:7 frme .: -..•'.:- rif.ii.ln- 
.fr-~: i- -if; ii 1 :r fi; :;fi .in.::. :r .:: :i :r n rr i:; ::' :if =ili 
in is. rriil-. n 1 :rnil-f- ?•: Tif ::f 1 : " f in If i ii::if 7 i 1 1 i;rvi 
:r fx:'nrifi is r if-:: 1. ' -•-::'- if 7if :r ; i; .:" - :i .-..-. r :■: ill :r nlr'i: 
ii~f fi; if 1 n iff :if snf 7. 



49 I: shall and may be lawful &r any two or more Justieesof tbf 7 ■- f 
to take affidavits on oath or affirmation (which oath or affirmation snch Jus- 

::' r.f r:i.e> rf- 




::' -if illf -ir_:if 

..... . - 

•f ■:: :r n'if :: n; : r:r 



: i-i :7i: -i:i;.riln r- ;i .... i : : ' r s 7:- 
_ "ii .T-:-f " z'z 




:7 li-r:f :r 
■ i Trii: ii" 



Section II.) land-surveying. 333 

matter ortlring which shall be false or untrue ; every such person so offending 
shall, on conviction thereof, be deemed guilty of perjury, and shall suffer the 
like pains and penalties, to which persons guilty of wilful and corrupt perjury 
j are now liable. 

44. And be it enacted, that all and every of the powers, authorities, direc- 
tions, and provisions in this Act contained, shall be only so far effective and 
binding in each particular case, as they or any of them shall not be other- 
wise provided and enacted in any such Act hereafter to be passed as aforesaid. 



SPECIAL ACTS. 

Clauses selected from Special Acts, obtained for Inclosing cer- 
tain Commons and Waste Lands in the West Biding of the 
County of York. 

1. And be it enacted, That if any difference of opinion shall arise between 
the Commissioners appointed for setting outvaluing, dividing, and allotting 
the said commons and waste grounds, touching or concerning any matter or 
thing to be done by them by virtue of the said recited General Act, or this 
Act, the said Commissioners from time to time, and when and so often as such 
difference of opinion shall arise, shall, by writing under their hands, appoint 
some person (not interested in the premises) to be an umpire between them ; 
and the matter upon which such difference of opinion may arise, shall be set- 
tled and determined by such umpire, whose determination in writing shall 
be binding and conclusive. 

Provided always, that no person shall be capable of acting as an umpire, 
until he shall have taken the oath usual on such occasions. 

2. And be it enacted, That the said Commissioners and the said umpire shall 
be paid and allowed one guinea each, and no more, for every day they shall 
respectively travel or attend for the purpose of this Act, over and besides all 
their reasonable expenses at the times of such their journeys and attendances. 

3. And after the said Commissioners shall have set out and appointed the 
public carriage-roads and highways through and over the said commons and 
waste grounds, they shall set out such parts of the same, as they shall think 
proper, not exceeding five acres in the whole, to be used and enjoyed by the 
respective proprietors of the said lands, for the purposes of common watering- 
places for cattle, and getting stones and other materials for erectingand repair- 
ing buildings, bridges, walls, fences, and other works, for the reparation of the 
public and private roads. And the Commissioners shall in the next place 
assign, set out, allot, and award unto and for the lord of the manor, such part 
and parcel of the residue and remainder of the said commons and waste 
grounds, as shall in their judgment be equal in value to one full sixteenth part 



334 land-suiiveyixg. (Part VI. 

of the said residue of the said common ar. md-?, in lieu of and as a 

full recompense for all such right and interest in and to the soil of the said 
commons ar. 1 waste g rer expressly saved and re- 

served ; and that after set L:h part 

to the said lord of the manner, the Commissioners shall set out, assign, and 
allot the residue of the said commons an I waste grounds unto and amongst 
the said lord of the manor, and the said several other persons entitled to right 
of common or other rights and interests in and upon the said commons and 
waste grounds.accordingtothevalueoftheancientmessua. . >tfc ges, mills, 
old inclosed lands, tenements, and hereditaments, in respect whereof thev are 
so respectfully entitled to such right of common, as aforesaid, and according 
to the true and real value of such o : :r interests, as aforesaid, esti- 

mating lands at their full and fair value as they are worth to be let, and mes- 
50 .. - ? : : wires, mills, and other buildings at one-half only of such their re- 
spective values : hut in estimating the value of m w - ;■ : w. _■ w . .:: i mills, 
no regard shall be had to any additions or improvements made within forty 
years last past. Provided always, that no person shall be entitled to any al- 
lotment from the said commons and waste grounds, or any part thereof, for 
or in respect of any messuage, cottage, mill, or other building which shall be 
proved to the satisfaction of the said Commissioners to have been er : 
any time within sixty years next before the passing of this Act, uniw 
erection shall have been made upon the scite'of some ancient messuage, eot- 
: :, . will, or other building which shall have been originally erected sixty 
years or upwards before the passing of this Act. 

-4. Ail encroachments which at any time within twenty years now last past 
have been made upon the said commons and waste grounds shall be deemed 
part thereof, and shall be divided and allotted accordingly ; and in case any 
dispute or difference shall arise, touching any such encroachments or the 
extent thereof, such dispute or difference shall be determined by the said 
- 

5. Provided always, that the lands and grounds comprised in such encroach- 
ments shall be aliened to the persons who shall be in;: OBSession thereof, with- 
: : : e wrd to the value of such improvements as shall or may have been made 
thereon since such encroachments were made, in case the persons so in pos- 
session shall desire the same to be so allotted, and shall signify such desire by 
writing signed by them to be deliveredto the said Commissioners at th-ir first 
or second meeting to be holden in pursuance of this, and the said general Act ; 
and the value of such encroachments shall be deducted from the allotments 
to which such persons shall be entitled under this Act, unless it shall happen 
that the value of such encroachments respectively (quantity and quality con- 
sidered) shall be greater than the allotments to which such persons shall be 
entitled by virtue of this and the said recited General Act : and in that case 
proportionable part only of such encroachments shall be deducted therefrom 



Section II. J LAND-SUltVEYING. 335 

and the residue thereof shall be sold by the said Commissioners ; and if the 
persons in possession of such encroachments shall not be entitled to any allot- 
ments, then the whole of such encroachments shall be sold by the Commis- 
sioners, and conveyed by them in fee simple to the purchaser or purchasers 
thereof, and the money arising from such sales shall be applied towards de- 
fraying the expenses of obtaining and executing this Act. 

6*. And from and immediately after the passing of this Act until the ex- 
ecution of the award of the said Commissioners, it shall not be lawful for any 
persons whomsoever to grave, dig, get, pare, cart, or carry away any sods 
or turves from any part of the commons or waste grounds aforesaid ; and 
every person so doing, shall for every such offence forfeit and pay any sum 
not exceeding twenty shillings. 

7. And be it further enacted, That no sheep or lambs shall be kept in any 
of the new inclosures (except such as are not fenced by quicksets) during the 
space of nine years from the execution of the said award, unless the persons 
keeping such sheep or lambs do, at their own expense, fence their neighbour's 
quicksets, adjoining the inclosures where such sheep or lambs shall be kept, 
so as to prevent any damage being done to such quicksets by such sheep or 
lambs. 

8. And be it further enacted, That convenient gaps and openings shall be 
left in the fences and inclosures to be made by virtue of this Act, during 
such time as shall be allowed and fixed for making such fences as aforesaid, 
for the passage of cattle, carts, and carriages in and through the same, 
unless the said Commissioners shall order and award to the contrary, and 
then for such time only as they shall so order and award. 

Note. — The foregoing clauses are not contained in the General Act. 



SECTION III. 

The Method of reducing Statute Measure to Customary, and 
vice versa. 

It has been before observed, that by custom the perch varies 
in different parts of England j and with it, consequently, varies 
the acre in proportion. 

In Devonshire and part of Somersetshire, 15 ; in Cornwall, 18 ; 
in Lancashire, 21 ; and in Cheshire and Staffordshire, 24 feet 
are accounted a perch. 

In the common field-lands of Wiltshire, and in some other 
counties, there is a customary measure of a different nature, viz. 
of 120, instead of 160, statute-perches to an acre ; consequently. 



336 land-surveying. (Part VI. 

30 perche9 of statute-measure, make I rood of customary, or 
3 statute-roods 1 acre. 

In some places, an acre of this measure, is called a day-work, 
or day's-work of land. 

Note. — The utility of the following Problems will appear obvious, when we 
consider that in many places land is not only reaped and farmed, but also 
bought and sold by customary-measure. 

Besides, when persons have the contents of their estates in statute-measure, 
it is frequently necessary to reduce them to the customary-measure of the 
place ; and on the contrary, when the contents are in customary -measure, it 
may be desirable to reduce such contents to statute-measure. 



General Rules for reducing Statute-Measure to Customary ', and 
the contrary. 

Rule 1. — To reduce statute-measure to customary ; multiply the 
number of perches, statute-measure, by the square feet in a square 
perch, statute-measure ; divide the product by the square feet 
in a square perch, customary-measure, and the quotient will 
be the answer in square perches. 

Rule 2. — To reduce customary-measure to statute, multiply the 
number of perches, customary-measure, by the square feet in a 
square perch, customary-measure; divide the product by the 
square feet in a square perch, statute-measure, and the quotient 
will be the answer in square perches, which reduce to roods and 
acres by dividing by 40, and by 4. 

Note 1. — It is scarcely necessary to remark that the length of any perch mul- 
tiplied by itself, will give the number of square feet in a square perch of the 
same measure ; hence we have 16.5 x 16.5 = 272.25, the statute perch ; 
15 x 15 = 225, the Devonshire and Somersetshire perch ; 18 x 18 = 324, 
the Cornwall perch ; 21 x 21 = 441, the Lancashire perch ; and 24 x 24 = 
576, the Cheshire and Staffordshire perch. 

2. — It may also be observed that 4840 square yards make 1 statute acre ; 
4000 make 1 Devonshire or Somersetshire acre ; 5760 make 1 Cornwall acre ; 
7840 make 1 Lancashire acre ; and 10240 square yards make 1 acre of the 
customary-measure of Cheshire or Staffordshire. 



Section III.) land-surveying. 



337 



PROBLEM I. 

To reduce Statute Measure to the Devonshire and Somersetshire 
Customary Measure, of 15 Feet to a Perch, and vice versa. 

TABLE I. 



Stat. 


Customary. 


Stat. 


Cust. I 


Stat. 


Cust. 


A. 


A. 


R. P. 


P. 

1 


R. P. 


P. 

21 


R. P. 

25.4 


1 


1 


33.6 


1.2 


2 


2 


1 27.2 


2 


2.4 


22 


26.6 


3 


3 


2 20.8 


3 


3.6 


23 


27.8 


4 


4 


3 14.4 


4 


4.8 


24 


29.0 


5 


6 


8.0 


5 


6.0 


25 


30.2 


6 


7 


1 1.6 


6 


7.2 


26 


31.4 


7 


8 


1 35.2 


7 


8.4 


27 


32.6 


8 


9 


2 28.8 


8 


9.6 


28 


33.8 


9 


10 


3 22.4 


9 


10.8 


29 


35.0 


10 


12 


16.0 


10 


12.1 


30 


36.3 


20 


24 


32.0 


11 


13.3 


31 


37.5 


30 


36 


1 8.0 


12 


14.5 


32 


38.7 


40 


48 


1 24.0 


13 


15.7 


33 


39.9 


50 


60 


2 0.0 


14 


16.9 


34 


1 1.1 


100 


121 


0.0 


15 
16 
17 


18.1 
19.3 
20.5 


35 

36 
37 


1 2.3 

1 3.5 

1 4.7 


Stat. 


Customary. 


R. 

J 




R. P. 


18 
19 


21.7 
22.9 


38 
39 


1 5,9 
1 7.1 


1 8.4 


2 




2 16.8 


20 


24.2 






3 




3 25.2 











Note 1. — To reduce customary -measure, of 15 feet to a perch, to statute, 
multiply the number of square links, customary-measure, by .826447, and 
the product will be the answer in square links, which must be brought into 
acres, roods, and perches. (See a table of square links in the first Section.) 

2. — When it is intended to find the area of an estate in customary-mea- 
sure only, it is generally thought most convenient to take the dimensions by 
a chain properly adapted for that purpose. The Devonshire and Somer- 
set chain is 60 feet ; the Statute-chain 66 feet ; the Cornwall chain 72 feet ; 
the Lancashire-chain 84 feet ; and the Cheshire and Staffordshire chain 
96 feet in length. Each of these chains is divided into 100 equal links, in 
the same manner as the statute-chain; consequently, the customary-mea- 
sure is found by the same rules as the statute-measure. 

z 



338 LAND-SURVEYING. (Part VI. 

3. — It may also be observed that the Devonshire and Somerset link is 7.2 
inches ; the Statute link 7.92 inches ; the Cornwall link 8.G4 inches ; the 
Lancashire link 10.08 inches ; and the Cheshire and Staffordshire link is 
11.52 inches in length. 



EXAMPLES. 

1. In 25 a. 2r. 20p. statute, how many acres, &c. customary - 
measure ? 

BY RULE 1. 
A. R. p. 

2.5 2 20 
4 

102 

40 



15 x 15 — 225)1116225.00 
900 4 
.2162 . 
2025 



4100 
272.25 = 16.5 x 16.5 
20500 

8200 
8200 
28700 
8200 4?0 



4.96,1 
124 1 



31 A - ° R - 1p - Ans- 



. 1372 
1350 



.225 
225 





BY THE TABLE. 




A. 


R. 


p. 


20a. 


= 24 





32 


5a. 


== 6 





8 


2r. 


= — 


2 


16.8 


20p. 


= — 





24.2 




31 





1 Ans 



Section III.) land-surveying. 339 

2. In 31a. Or. 1p. customary, how many acres, &c. statute- 
measure ? 



BY RULE 2. 

A. R. P. 
31 1 

4 

124 
40 



4961 
225 

24805 
9922 
9922 



272.25)1116225.00 
108900 4 



410 



102.20 



2/225 25a. 2r. 20p. Ans. 

27225 - 



00 



BY THE NOTE. 

sq. links. 

30a. = 3000000 

1a. = 100000 

lp. = 625 



3100625 
. 82 6447 
21704375 
12402500 
12402500 
18603750 
6201250 
24805000 
25.62502.229375 
4 



2.50008 
40 



20.00320 Ans. 25a. 2r. 20p. 



3. In 159a. 3r. 26p. statute, how many acres, &c. customary- 
measure ? 

Ans> 193a. 1r. 39p. 
z2 



340 



land-surveying. (Pari VI 



PROBLEM II. 

. s Ut Meeuun to thi Cornwall C M 

of IS Feet to a Perch, and vice versa. 

TABLE II. 



Star. 
A. 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

20 

30 

40 

50 

100 

StoL 
R. 



CusTomarv. 
A. R. P. 




1 

2 

3 
4 
■5 
5 

6 

8 
16 
25 
33 
42 
84 



14.4 

28.8 

3.3 

17.7 

32.2 

21.0 

3.5.5 
9.9 

24.4 
8.8 

33.2 

17.6 
2.0 
4.0 



Customarv. 
R. P. 



33.6 

1 27.2 

2 20.8 



Stat. 


Cost 


P. 


P. 


1 


0.8 


2 


1.6 


3 


2.5 


4 


3.3 


.5 


4.2 


6 


5.0 


: 


5.8 


8 


<-.: 


9 


:.5 


10 




11 


9.2 


12 


10.0 


13 


io.g 


14 


ii.: 


15 


12.6 


16 


13.4 


i; 


14.2 


18 


15.1 


19 


i5..;' 


20 


16.8 



Stat. Oust 
P. P. 



21 
22 
23 
24 
25 
26 
27 
2s 
29 
30 
31 
32 
33 
34 
35 
36 
3? 
38 



17.6 
18.4 

19.3 
20.1 

21.0 
21.8 
22.6 
23.5 
24.3 
25.2 
26.0 
26.8 
27.7 
2S.5 
1 A 
3'"'. 2 
31.0 
31.9 
32.7 



Xote. — To reduce customary-measure, of 18 feet to a perch, to statute, 
multiply the number of square links, customary-measure, by 1.19, and the 
product will be the answer in square links, 



Section III.) land-surveying. 341 



EXAMPLES. 

1. Reduce 56a. 3r. 36p. statute, to customary-measure. 

BY RULE 1. 
A. R. P. 

56 3 36 

4 

227" 
40 

9116 
272.25 

45580 
18232 
18232 
63812 
18232 



18 X 18 = 324)2481831.00 

2268 A 



4,0 
7659.9 



191 19.9 

2138 47a 3r i9.9p. Ans. 
1944 

•1943 
1620 



• 3231 
2916 



3150 
2916 

• 234 








BY THE TABLE. 




A. R. P. 


50a. 


= 42 2 


6a. 


= 5 6.6 


3r. 


= 02 20.8 


36p. 


= 00 30.2 




47 3 19.6 Ans 



z3 



342 Land-surveying. (Part VI 

2 - B* ' ' *■ - " bomai -measure. 



BY RULE 2. 
A. R. p. 

4 
4-0 



3 
124 



I 

1532 

55 

."::■:" i^if^.oo nil o 



246025 r — 



56a. Sit. 36i Am 

- --'"■ ======== 

43650 

--225 



i : a -: 



:be note. 

.inks. 

= 4000000 

~. = '00000 

3ft. = 75000 

20p. = 125: • 

*7875( 



875 
t7875 
47875 

4 



J.88i 

4 



35.40000 Ana : : a. 3r. -S; 

'-■ 1; - . ■ . .- . r how many = 

customarv-me&V- 

Ans. 223a. Or. 



Section III.) land-surveying, 



343 



PROBLEM III. 

To reduce Statute Measure to the Lancashire Customary Measure, 
o/2\ Feet to a Perch, and vice versa. 





TABLE III. 






Stat. 


Customary. 


Stat. 


Cust. 


Stat. 


Cust. 


A. 
1 


A. R. P. 


P. 

1 


P. 


P. 

21 


P. 


2 18.7 


0.6 


12.9 


2 


1 37.5 


2 


1.2 


22 


13.5 


3 


1 3 16.3 


3 


1.8 


23 


14.1 


4 


2 1 35.0 


4 


2.4 


24 


14.8 


5 


3 13.8 


5 


3.0 


25 


15.4 


6 


3 2 '32.6 


6 


3.7 


26 


16.0 


7 


4 1 11.4 


7 


4.3 


27 


16.6 


8 


4 3 30.1 


8 


4.9 


28 


17.2 


9 


5 2 8.9 


9 


5.5 


29 


17.9 


10 


6 27.7 


10 


6 1 


30 


18.5 


20 


12 1 15.4 


11 


6.7 


31 


19.1 


30 


18 2 3.1 


12 


7.4 


32 


19.7 


40 


24 2 30.8 


13 


8.0 


33 


20.3 


50 


30 3 18.5 


14 


8.6 


34 


20.9 


100 

Stat. 
R. 

1 


61 2 37.0 


15 
16 
17 


9.2 

9.8 
10.4 


35 

36 
37 


21.6 
22.2 

22.8 


Customary. 
R. P. 


18 
19 


11.1 
11.7 


38 
39 


23.4 
24.0 


24.7 


2 


1 9.4 


20 


12.3 






3 


1 34.1 











Note 1. — To reduce customary-measure, of 21 feet to a perch, to statute, 
multiply the number of square links, customary-measure, by 1.62, and the 
product will be the answer in square-links. 



2.— As the lineal Irish perch is 21 feet, and the Irish square perch 441 
feet ; the method of reducing English to Irish, or Irish to English measure 
is precisely the same as shewn in this Problem. 

z 4 



344 laxd-sulvzying. fPmi VI 



EXAMPLES. 

11:1 -rate, how manr acres. &c. 



BY RITLE 1 . 


A. 


R. P. 


36 


i ic 


1 




rr 7 




w 




5810 




272^5 




29054 




1 1 5 1 




::-": 




--\-r 




1 1 : : 


M 


1581772 5( 35S 


132S 4 
.2581 


: . : - 


i - - - - 


2205 


- - A . I;. 


3Si: 




3528 




. 2992 




. — 




." 1 :" 5 




::~- 




17a 




- V THE TABLE, 


A. 


B, P. 


.. = If 


2 3.1 


- = 3 


- J..- 


IB. = 


24 


'-'.:- = 





22 


1 26.5 Ails. 



Ar - 



Section 111,) land-surveying. 345 

2. Reduce 22a. 1r. 27p. customary, to statute-measure. 



BY RULE 2. 


A. 


R. 


P. 


22 


1 


27 


4 






89 






40 






3587 






441 







3587 
14348 
14348 



4,0 



272.25)1581867.000,581,03 

136125 41 145* 1 0. 3 

..28170 
27225 



94500 

816*75 

12825 



BY NOTE 1. 

sq. links. 
20a. = 2000000 

2a. = 200000 

1r. = 25000 
27p. = 16875 

2241875 
1.62 

4483750 
13451250 
2241875 

36.31837.50 
4 

1.27348 
40 

10.93920 Ans. 86a. 1r. 10.9p. 



3. Reduce 116a. 3r. 32p. English measure, to Irish measure. 

Ans. 72a. Or. 31 p. 



346 



EYING. 



Pari 



PROBLE! I : 

stomary Measure, cf 24 Feet to a Perek, and -rice Ye: 

TABLE IV. 



>----. 


o 


l^T " 


hit v. 


>i: 


Cast. 


Srat, 


C-5T. 


A 


3 


R. 


P. 


"?.' 


P. 


P. 


P. 




1 




1 


■:". - 


1 
2 


0.-=- 


_ g 


: : : 




I 




:■;.? 


_ : 


1.4 


-3 


10.? 


4 


1 




22 :' 


1 


1.? 


24 


11.3 




2 


1 


is .: 


5 




25 


11.7 




2 


- 

o 


: ? 


6 


2.S 


26 


IS I 


- 


: 


I 


9.3 


J 


:-.: 


27 


12.7 


> 




n 


■:. 


S 




25 


13.1 




4 


1 


0.6 


- 


. 


29 


i ; : 


10 


4 


2 


3'?. 2 


10 




30 




:: 


9 


1 


:. i 


II 


. 5 


31 




! 


14 





I'S.-f' 


12 




:- 


15 : 


40 


18 


•3 


24.8 


11 


6.1 




I : : 


:" 


23 


o 


.:.: 


14 


6.6 


M 


1-f.O 


::" 


*7 


1 


- 


15 

16 

i: 




35 


13.4 
1*.0 




Cus:: :-.- 


R. 


i\. 


r. 


1 s 


5.4 


33 


17 

15.3 


: 


o 


i - 


•:■ 


37-S 


2 ; 


3 1 






5 




i 


ie.7 









Aofe. — To lednee cnstomaiy-roeasaie, of 24 feet to a perch, to statute, 

nildrlv :cf r"ir_r;r ::' ; ::itIh.I: = . •: _-::n^r- ■■~-.:i — i. v ; - .".I:". -il 



Section III.) land-surveying. 347 



EXAMPLES. 

1. Required the number of acres, &c. customary-measure, in 
269a. 2r. 12p. statute -measure. 

BY RULE 1. 
A. R. P. 

269 2 12 
4 

1078 
40 

43132 
272.25 

215660 
^6264 
86264 
301924 
86264 4Q 

24 x 24 = 576)11742687.0012038.6.6 
1152 4| 509.26.6 

. . 2226 127a. 1r. 26.6p. Ans. 

1728 

. 4988 
4608 



.3807 
3456 

.3510 
3456 



54 



BY THE TABLE. 


A. 


R. P. 


200a. = 94 


2 4 


50a. = 23 


2 21 


30a. = 4 


2 36.2 


9a. = 4 


1 0.6 


2r. = 


37.8 


12p. == 


5.6 



127 1 25.2 Ans. 



348 land-surveying. (Part VI, 

2. In 127a. 1b. 26p. customary, how many acre?. &c statute- 
measure ? 

BY RULE 2. 
A. R. P. 

127 1 20 

4 

509 
40 



20386 
57 6 



122316 
142702 
101930 



4,0 



272.25)11742336.00 4313 0.7 
108900 



4 10 78 10.7 
' ' ff?.?? 269a. 2r. IO.Tp. An?. 

OlOiO — 

. 35586 
27225 

.83610 
81675 



193500 
190575 



2925 



BY THE NOTE. 




sq. links, 


00a. 


= 10000000 


20a. 


= 2000000 


7a. 


= 700000 


1R. 


= 25000 


26p. 


= 16250 




12741250 




2,4157 




89188750 




6370625 




1274125 




1274125 


S 


548250 



269.56662.6250 

4 

2.26648 
40 



10.65920 Ans. 269A. 2p. 10.6p. 



Section III.) land-surveying. 349 

3. Reduce 587a. 3r. 39p. statute, to customary-measure. 

Ans. 277a. 3r. 27p. 



PROBLEM V. 

To reduce Statute Measure to the Wiltshire customary Measure, 
of 120 Perches to an Acre, and vice versa. 

Rule 1. — To reduce statute-measure to customary, divide 
the number of perches, statute- measure, by 120, and the 
quotient will be acres ; then divide the remainder by 30, and 
the quotient will be roods ; and the last remainder, if any, will 
be perches. If the first remainder be under 30, it will be 
perches, and there will be no roods in the answer. 

Rule 2. — To reduce customary-measure to statute, divide the 
number of perches, customary-measure, by 160, and the quo- 
tient will be acres ; then, divide the remainder by 40, and the 
quotient will be roods ; and the last remainder, if any, will be 
perches. If the first remainder be under 40, it will be perches, 
and there will be no roods in the answer. 

Note 1. — To bring customary acres, &c. into perches, multiply the number 
of acres by 120, and the number of roods by 30 ; these two products, added 
to the number of given perches, will be the number of perches required. 

2. — In some parts of England, land is not only reaped and farmed, but also 
bought and sold by this measure ; and as the customary acre of 120 statute 
perches, or three statute roods, is frequently denominated a day's work or day- 
work of land, Surveyors are sometimes required to return the areas of estates 
in day's works, roods, and perches. 



350 



LAND-SURVEYING 



(Part VI 






TABLE V. 



Stat. 


Customary. 


Stat. 


Oust. 


Stat. 


Cust. j 


A. 


A. 


R. 


P, 


P. 


R. P. 


P. 


P. P. 


1 


i 


1 


10 


1 


1 


21 


21 


2 


2 


2 


20 


2 


2 


22 


22 


3 


4 








3 


3 


23 


23 


4 


5 


1 


10 


4 


4 


24 


24 


5 


6 


2 


20 


5 


5 


25 


25 


6 


S 








6 


6 


26 


26 


7 


9 


1 


10 


7 


7 


27 


27 


8 


10 


2 


20 


8 


8 


28 


28 


9 


12 








9 


9 


29 


29 


10 


13 


1 


10 


10 


10 


30 


1 o 


20 


26 


2 


20 


11 


11 


31 


1 1 


30 


40 





o 


12 


12 


32 


1 2 


40 


53 


1 


10 


13 


13 


33 


1 3 1 


50 


66 


2 


20 


14 


14 


34 


1 4 


100 


133 


1 


10 


1.5 
16 
17 


15 
16 
IT 


35 
36 

37 


1 5 
1 6 
1 7 


Stat. 


Customary. 


R. 

1 


A. 


R. 


P. 


18 

19 


• 
18 
19 


38 
39 


1 8 
1 9 





1 


10 


2 





2 


20 


20 


20 






3 


1 

















Xote. — In adding up the numbers taken from the above table, you must 
divide the number of perches by 30, and the number of roods by -1 ; because 
30 perches of this measure make 1 rood, and 4 roods 1 acre, or 1 day's work, 

EXAMPLES. 

1. In 165a. 3r. 26p. statute-measure, how many acres, &c. 
customary ? 

BY RULE I. 
A. R. P. 

165 3 26 



663 

40 

120)26546(221 
240 



254 
240 



146 
120 
726 Ans. 221A. Or. 



26'p. 



Section III.) land-surveying. 351 



BY THE TABLE. 

A. R. P. 

100a. = 133 1 10 

50a. = 66 2 20 

10a. = 13 1 10 

5a. = 6 2 20 

3r. = 10 

26p. = 26 

221 26 Ans. 



2. Required the number of acres, &c. statute-measure, in 
221a. Or. 26p. customary. 

by rule 2. 

p. 

221 X 120 = 26520 
26 = 26 



160)26546(165 
160 
1054 
960 



..946 

800 
40)146(3 

120 

?26 Ans. 165a. 3r. 26p. 



3. In 265a. 2r. 24p. statute, how many acres, &c. customary 
measure ? 

Ans. 354a. Or. 24p. 



GENERAL RULES 

For constructing the foregoing Tables, and for finding the Mul- 
tipliers given in the Notes. 

Rule 1. — Divide the number- of square feet in an acre, statute-measure, 
by the number of square feet in an acre, customary -measure, and the quotient 
will be an acre and decimals, or decimals of an acre. Multiply this quotient 



3 52 



LAI 



EYING, 



(Part VI 



by 2, and the product will be the acres and decimals, customary-mowne, 
in 2 acres, statute-measure. Bring the decimals to their proper quantity, 
and you will have the acres, roods, and perches, customary -measure, in 2 
acres, statute-measure. In a similar manner you must proceed with 3 
acres, 4 acres, &e. 

Rule 2. — Divide the number of square feet in a rood, statute-measure, by 
the number of square feet in a rood, customary-measure, and the quotient 
will be a rood and decimals, or decimals of a rood. This quotient being 
multiplied by 2, the product will be the roods and decimals, customary - 
measure, in 2 roods, statute-measure. In a similar manner you must pro- 
ceed with 3 roods. 

Rule 3. — Divide the number of square feet in a perch, statute-measure, 
by the number of square feet in a perch, customary-measure, and the 
quotient will be a perch and decimals, or decimals of a perch. Multiply 
this quotient by 2, and the product will be the perches and decimals, cus- 
tomary-measure, in 2 perches, statute-measure. In a similar manner you 
must proceed with 3 perches, 4 perches, &c. 

Rule 4. — To find the multipliers given in the notes, say, as the number 
of square feet in an acre, statute-measure, is to an acre, so is the number 
of square feet in an acre, customary-measure, to the multiplier. 

Or, divide the number of square feet in a perch, customary-measure, by 
the number of square feet in a perch, statute-measure, and the quotient 
will be the multiplier. 

JN'ofc. — Table V. was constructed by Role 1, given in tee last Problem. 



REMARKS. 

1. If a tenant rents a farm of 100 acres, reckoning 120 
perches to an acre of tenantry measure, which is but 3 roods, 
statute-measure ; he loses 1 acre in 4, or 25 acres in the 
whole, which reduces his farm to 75 acres, statute -measure. 

2. If a tenant takes a farm, in Devonshire or Somersetshire, 
of 100 acres, at the customary-measure of 15 feet to a perch ; 
he loses nearly 1 statute acre in 6 customary acres, or IT 
acres, 1 rood, 17 perches, in the whole, which reduces his farm 
to 82 acres, 2 roods, 23 perches, statute -measure. 

3. If a tenant rents a farm of 1 00 acres> in Cornwall, at the 
customary-measure of 1 8 feet to a perch ; he gains about 1 
statute acre in 5 customary acres, or 19 acres, roods, 1 perch, 
in the whole ; consequently, his farm contains 119 acres, 
roods, 1 perch, statute-measure. 

■i. If a tenant takes a farm of 100 acres, in Lancashire, 
reckoning 21 feet to a perch, customary-measure; he gains 



Section III.) land-surveying. 353 

nearly 2 statute acres in three customary acres, or 61 acres, 
3 roods, 37 perches, in the whole; hence, his farm contains 161 
acres, 3 roods, 37 perches, statute-measure. 

5. If a tenant rents a farm of 100 acres, in Cheshire or Staf- 
fordshire, reckoning 24 feet to a perch, customary-measure ; he 
gains nearly 16 statute acres in fourteen customary acres; or 
111 acres, 2 roods, 1 1 perches, in the whole ; hence, his farm 
contains 211 acres, 2 roods 11 perches, statute-measure. 

6. Three acres, statute-measure, are equal to 4 acres, Wilt- 
shire measure. — Fire acres, statute-measure, are equal to 6a. 
Or. 8p. Devonshire and Somersetshire measure. — Six acres, 
statute-measure, are equal to 5a. Or. 6£p. Cornwall measure. — 
Five acres, statute-measure, are equal to 3a. Or. 14p. Lancashire 
measure. — Thirty acres, statute-measure, are equal to 14a. Or. 
28|p. Cheshire measure. 

SCOTCH MEASURE. 

In Scotland, land is generally measured by a chain of 74 feet 
in length, which is divided into 100 equal links, the same as 
the English chain. 

The area is given in acres, roods, and falls; 342.25 square 
feet making 1 fall, 40 falls 1 rood, and 4 roods 1 acre. 
TABLE YI. 
A Table of Scotch Lineal Measures. 



Inches. 
8.88 


1 Lk. 








12 


1.35 


1 Foot. 


1 Ell. 




3? 


4.16 


3.08 






222 


25 


18.5 


6 


l Rd. 






88.8 


100 


74 


24 


4 


1 Chain. 




71040 


8000 


5920 


1920 


320 


80 


1 Mile. 



Note. — It appears by comparing the above Table with that given in Part III., 
that the Scotch ell is 1 inch more than the English yard ; and the Scotch 
mile 640 feet more than the English mile ; but by a statute of James II., it 
was enacted that the Scotch mile, like the English, should contain 1760 yards. 

A a 



354 



LAND-SURVEYING. 

TABLE VII. 

^4 Table of Scotch Square Measures, 



(Part VI. 



Sq. Inches. 

78.8544 

144 


1 Sq. Lk. 






1.82 


1 Sq. Ft. 




•v 


1369 


17.36 


9.51 


IS. Ell. 






49284 


625 


342.25 


36 


IS. Fall. 






1971360 


25000 


13690 


1440 


40 


1 S.Rd. 




7885440 


100000 


54760 


5760 


160 


4 


■ 

lS.Acre. 



Note. — By comparing the above Table with that given in Part III., W8 
find that the Scotch fall contains 70 square feet more than the English statute 
perch ; and the Scotch acre 1 1200 square feet more than the English statute 
acre ; hence 1089 Scotch acres are equal to 1369 English acres. 

TABLE VIII. 

A Table fen* reducing English to Scotch Measure, 



Eng. 


Scotch. 


Eng. 


Scotch. 


En£. 


Scotch. 


Acs. 


A. 


R. F. 


P. 


Falls. 


P. 


Falls. 


1 





3 7.3 


1 


0.8 


r 21 


16.8 


2 


1 


2 14.5 


2 


1.6 


22 


17.5 


3 


2 


1 21.8 


3 


2.4 


23 


18.3 


4 


3 


29.1 


4 


3.2 


24 


19.1 


5 


3 


3 36.4 


5 | 


4.0 


25 


20.0 


6 


4 


3 3.7 


6 


4-8 


26 


20.8 


7 


5 


2 10.9 


7 


5.6 


27 


21.5 


8 


6 


1 18.2 


8 


6.4 


28 


22.3 


9 


7 


25.5 


9 


7.2 


29 


23.1 


10 


7 


3 32.8 


10 


8.0 


30 


24.0 


20 


15 


3 25.5 


11 


8.8 


31 


24.8 


30 


23 


3 18.3 


12 


9.6 


32 


25.4 


40 


31 


3 11.0 


13 


10.3 


33 


26.2 


50 


39 


3 3.8 


14 


11.1 


34 


27-0 


100 


79 


2 7.5 


15 
16 
17 


12.0 
12.8 
13.5 


35 
36 
37 


27.8 
28.6 
29.4 


Eng. 




Scotch 


Rds. 




R. F. 


18 

19 


14.3 
15.1 


38 
39 


30.2 
31.0 


1 




31.8 


2 




1 23.6 


20 


16.0 






3 




2 15.5 











Section 111.) land-surveying. 355 

Note 1 . — The General Rules given in the beginning of this Section, may 
be applied in reducing English to Scotch, or Scotch to English measure. 

2. — Scotch measure may also be reduced to English statute-measure, by 
multiplying the number of square links, Scotch measure, by 1.2571 ; and 

the product will be the answer in square links. 

i 

EXAMPLES. 

1. In 45a. 2r. 23p. English statute-measure, how_ much 
Scotch measure ? 





BY RULE I. 




A. 


R. P. 




45 


2 23 




4 






182 






40 






7303 






272.25 


= 16,5 




36515 






14606 






14606 






51121 






14606 


4,0 


342 


.25)1988241.75 
171125 a 


580,9.3 
i ±k q r- 



X 16.5 



? 7 J 9 ?} 36a. 1r. 9.3f. An*. 



319175 
308025 



111500 
102675 

. . 8825 





BY TABLE VIII. 




A. R. F. 


40a. 


= 31 3 11 


5a. 


= 33 36.4 


2r. 


= 1 23.6 


23p. 


= 00 18.3 



36 1 9.3 Ans. 



2. In 36a. 1r. 9.3f. Scotch measure, how much English mea- 
sure ? 

A a 2 



356 land-surveying. (Part VI. 



BY 


RULI 


.2, 


A. 


R. 


F, 


36 


1 


9.3 


4 







145 

40 

5809.5 
342.25 

290465 
116186 
116186 
232372 
174279 



272.25)1988232.925 
190575 4 



7302.9 



182 22.9 

45a. 2r, 22. yp. Am 

81675 ■ 



80792 
54450 

263425 
24502 5 

18400" 



BY NOTE. 2 

30a. = 3000000 
6a. = 600000 
1r. = 25000 
9p. = 5625 
^p. = 187.5 
3630812.5 
1.2571 
36308125 
254156875 
181540625 
72616250 
36308125 

45.64294.39375 

4 

2.57176 
40 



22.87040 Am 45a. 2r. 22.gr. 



Section III.) land-surveying. 357 

3. Reduce 102a. 3r. 38p. of English statute-measure, to 
Scotch measure. Ans. 81a. 3r. 27.7p. 

4. In 52a. 2r. 3Gf. Scotch measure, how many acres, &c. 
English measure ? Ans. 66a. Ir. 5 p. 



IRISH MEASURE. 

In Ireland, land is measured by a chain of 84 feet in length, 
which is divided into 100 equal links, the same as the English 
chain. 

The area is given in acres, roods, and perches, the same as in 
England; but the Irish perch contains 168.75 square feet more 
than the English perch ; and 98.75 square feet more than the 
Scotch fall ; consequently, the Irish measure is greater than 
either the English or the Scotch measure. 



TABLE IX. 

A Table of Irish Lineal Measures. 



Inches. 
10.08 


1 Link. 






12 


1.19 


1 Ft. 






36 


3.57 


3 


1 Yd. 






252 


25 


21 


7 


lPch. 






1008 


100 


84 


28 


4 


lChn. 




80640 


8000 


6720 


2240 


320 


80 


1 Mile. 



Note. — By comparing the above Table with that given in Part III., we 
find that the Irish mile is 480 yards more than the English mile J hence 11 
Irish miles are equal to 14 English miles. 

a a 3 



358 



land-surveying. (Fart VI. 



TABLE x. 



A Table of Irish Square Measures. 



Sq. Indies. 
| 101.6064 


1 Sq. Lk. 






144 


1.42 


1 Sq. Ft. 


1 




1296 


12.78 


9 


lS.Yd. 
49 


1 


63504 


625 


441 


lS.Ph. 1 




2540160 


25000 


17640 


1960 


40 lS.Rd. 




10160640 


100000 


70560 


7840 


160 


4 


IS. Ac! 
• 



Note 1. — By comparing the above Table with that given in Part III., we 
find that the Irish perch contains 168.75 square feet more than the English 
statute perch ; and the Irish acre 3000 square yards more than the English 
acre j hence 121 Irish acres are equal to 196 English acres. 

2. — Irish measure may be reduced to English, or English measure to Irish, 
by Problem III. 

3. — Scotch measure may be reduced to Irish, or Irish measure to Scotch, 
by the following rule : As the square feet in a square perch of the required 
measure, is to the given area in perches ; so is the square feet in a square 
perch of the given measure, to the required area in perches. 

4. — The rule given in the last note, is the substance of the two General 
Rules given in the beginning of this Section : and will hold good for all kinds 
of measures. 



The Rules given in this Wo?~k,for Jin ding the Areas of Figures, 
and Dividing Land, are applicable in all cases of Land- 

Surveying. 

As both the Scotch and Irish chains are divided into 100 
equal parts, the same as the English chain ; it is manifest that 



Section III.) land-surveying. 359 

the Rules given in this Work, for finding the areas of figures, 
and for laying out, parting-ofF, and dividing land, are applicable 
in all cases of Surveying, whether the dimensions be taken with 
the English, Scotch, or Irish chain. 

They also hold equally true, if the dimensions be taken in 
yards, tenths, and hundredths ; in feet and tenths ; or in any 
other denominations. 



EXAMPLES 



ENGLISH, SCOTCH, and IRISH MEASURES. 

1. The base of a triangular field, measured by the English 
chain, is found to be 1252 links, and the perpendicular 684 
links ; what is the area of the field, in statute-measure ? 

links. 
1252 

684. 

5008 -1 . 

10016 
7512 



2) 856368 

4.28184 
4 

1.12736 

40 

5.09440 Ans. 4A. Ir. 5p. 



2. Reduce 4a. Ir. 5p. English measure, to Scotch and Irish 
measure. 

Reduced to Scotch Measure by Table VIII* 

A. R. F. 

4a. = 3 29.1 
Ir. = 31.8 
5p. =0 4.0 



3 1 24.9 Ans. 



A a 4 



360 land- surveying. (Part VI. 

Reduced to Irish Measure, by Talk III. 





A. 


it. 


p. 


4a. 


= 2 


1 


35.0 


lR. 


= 





24.7 


5p. 


= 





3.0 




2 


2 


22.7 Ans. 




— 







3. The base of a triangular field, measured by the Scotch 

chain, is 1252 links, and the perpendicular 084 links; required 

the area of the field in Scotch measure. 

links. 
1252 

084 

5008 
10016 
7512 

2)856308 

4.28184 

4 



1.12730 

40 



5.09440 Ans. 4a. 1r. 5p. 



Note. — Here the area is the same as that found in the first example. 
4. Reduce 4a. 1r. 5f. Scotch measure, to English and Irish 
measure. 

Reduced to English Measure, by Note 2, under Table VIII. 

sq. links. 
4a. = 400000 
1r. = 25000 
5f. = 3125 
428125 
1.2571 
428125 
2990875 
2140025 
850250 
428125 



5.38195.9375 
4 



1.52780 
40 



21.11200 Ans. 5a. 1r. 21. 1p, 



Section III.) LAND-SURVEYING. 36 1 

Reduced to Irish Measure by Note 3, under Table X. 



A. R. 


F. 


4 1 


5 


4 




vT 




sq. ft. J5 


sq.ft. 


As 441 : 685 :: 


342.25 


342.25 




3425 




1370 




1370 




2740 




2055 4i0 




441)234441. 25j53,1.61 


2205 4 I 13 


16.1 


. 1394 3A 


. 1r. 16. lp. An&, 


1323 




~711 




441 




2702 




2646 




"565 




441 





124 

5. The base of a triangular field, measured by the Irish 

chain, is 1252 links, and the perpendicular 684 links; what is 

the area of the field in Irish measure ? 

links. 
1252 

684 



5008 
10016 
7512 

2)856368 

4.28184 

4 

1.12736 

40 

5.09440 Ans. 4a. 1r. 5p. 



Note. — Here the area is the same as that found in the first and third ex- 
amples, which proves that the Rules for finding the areas of figures hold 
good for all kinds of measures. 



o62 UNI- SO] LVKYTS P H VJ 

6. Redoce 4a. 1b. dp. Irish measure, to flogHiA and fit oil ■ 



!L- :.::::. 



F-. ; :-'.-■ ;■. £■■/ _'/ • ;/ . ■-. ." . V -. -. ■ /•_.', _T 



B. P. 
I ' 
I 

r: i_ ;,- :'- 

141 

685 

274 



- - - 1 ' - «o U 

4i 27 2 



27 225 



- 1 : . ; : 

i - - • 

: : _. ' 

".23625 



Reduced to Scotch Measure lu ." .nder TaV X 

r sq. p. sq. : 

K3 25 »5 :: 141 

I4J 

— 5 
*74 

!^ 1 



-7 - : 7 .i_ j 



_ _ f 

r 7 — 



The length of a rectangular field, measured by the English 
chain .. i its breadth 923 link*; required the 

area of the field, in English, Scotch, and Irisk measnre. 



Section III.) land-surveying. 363 

Ans.' 13a. Or. 39p. English measure ; 10a. 2r. 5. 6f. Scotch 
measure ; and 8a. Or. 2 8 p. Irish measure. 

8. A Land-Surveyor is required to measure a triangular field, 
and to return the area in English statute-measure ; but not 
having an English chain, he found the base of the field to mea- 
sure 1548 links, and the perpendicular 924 links, by a Scotch 
chain; required the area of the field in English statute-mea- 
sure. Ans. 8a. 3r. 38. 4p. 



GAD MEASURE. 

In some places the dimensions of land are taken, by farmers, 
workmen, &c. with a pole or staff of 8, 9, or 10 feet in length, 
called a Gad ; hence the square gad of 8 feet, contains 64 square 
feet ; the square gad of 9 feet, 81 square feet ; and the square 
gad of 10 feet, 100 square feet. 

When the area of a piece of land is wanted in gad -measure, 
the dimensions, taken in gads and feet, must be brought into 
feet ; from which the area, in square feet, may be obtained, by 
the rules already given. Divide this area by 64, 81, or 100, 
respectively; and the quotient will be the number of square 
gads ; and the remainder will be square feet. If the remainder 
be multiplied by 4, and divided as before, the quotient will be 
I, i, or | of a gad. 

If, however, the gad be decimally divided, the dimensions 
mil be taken in gads and tenths, and the rules will then give 
the area, in square gads and decimal parts. 

The decimals may be reduced to their proper quantity by 
multiplying them by the number of square feet in a gad ; or to 
quarters of a gad, by multiplying them by 4, as before directed. 

Note 1. — Gad-measure may be reduced to English statute-measure, by the 
following Rule : As 272.25, the square feet in a square perch, statute-mea- 
sure, is to the given area in gads ; so is the square feet in a gad of the given 
measure, to the required area in perches. Or, divide the square feet in the 
given area, by 272.25 ; and the quotient will be the answer in square perches, 
statute-measure. 

2. — To reduce statute-measure to gad-measure, divide the given area in 



364 land-surveying. (Part VI. 

square feet, by the number of square feet in a gad \ and the quotient will 
be the answer in square gads. 

EXAMPLES. 

1. The length of a rectangular piece of land, measured with 
the eight-feet gad, is 45 gads, 5 feet ; and its breadth 21 gads, 
3 feet ; required its area in square gads. 



8x8 



G. F. 


G. F. 


45 5 


21 3 


8 


8 


365 


171 


171 




365 




2555 




365 




C4)62415)975g. 


15f. Ans. 


^7ft : — : — — 









481 




448 




335 




320 




. 15 rem. 





2. The area of a piece of ground, measured by the eight-feet 
gad, is found to be 975 gads, 1 5 feet; required its area in sta- 
tute-measure ? 

BY NOTE 1. 



G. F. 

975 15 
64 



3905 

5851 4 ?0 

272.25)62415.00| 22 ( 9.25 
54450 4 | 5 29 i 

79650 



54450 : 

252000 
245025 

69750 
54450 



153000 
136125 

7l6875 rem. 



1a. 1r. 29ip. Ans. 



Section III.) land-surveying. 365 

3. The area of a piece of land is 1a. 1r. 29|p. statute-mea- 
sure ; what will be its area in square gads, if it be measured 
by the eight-feet gad ? 



by note 2, 

A. R. P. 

1 1 29.25 
4 

40 



229.25 
272.25 

114625 

45850 
45850 
160475 
45850 

64)62413.3125(9750. 13.3F. Ans, 
576 =z= 

.481 
448 

~333 
320 



. 13.3 rem. 



4. The base of a triangular field, measured with the nine -feet 
gad, decimally divided, is 58.7 gads, and the perpendicular 
26.9 gads; required the area of the field, in gad, and also in 
statute-measure ? 

Here, 58.7x26.9=1579.03; and ^ — = 789.515, the area 

in gads; and by Note 1, as 272.25 feet : 789.515 gads :: 81 feet 
: 234.89 perches = 1a. 1r. 34.89p. the area in statute-mea- 
sure. 

5. The length of eight lands, forming a furlong in an open 
field, is found, by the ten-feet gad, to be 118.7 gads, and their 
breadth 12.4 gads ; what is the area of the furlong ? 

Ans. 1471.88 gads = 3a. Ir. 20.6p. statute-measure. 

6. The diagonal of a trapezium measures 56.2 gads, by the 



366 LAND-SURVEYING. (Part VI. 

ten-feet gad, one of the perpendiculars 21.4 gads, and the other 
18.3 gads; required the area of the trapezium? 

Ans. 11 15. 57 gads = 2a. 2r. 9.?p. statute-measure. 



ESTIMATING LAND BY THE MILE. 

The Method of making a rough Calculation of the Number of 
Acres contained in a Common, Moor. Lordship, County, or 
Kingdom, 

Endeavour to ascertain, in miles, as nearly as you can, either 
by your own observations, or from the information of others, 
the mean length and breadth of the land to be estimated ; then 
multiply the length by the breadth, and the product will be the 
area in square miles. Multiply this area by 640, the number 
of acres in a square mile ; and the product thus obtained will 
be the area in acres, according to this method of calculating. 

Note 1. — The mean length and breadth of a county or a kingdom, may be 
found from a map, in the following manner : Measure several lengths, by the 
scale of miles, upon the map ; add them together ; and divide their sum by 
their number, for a mean length. A mean breadth may be obtained by a 
similar process, 

2. — The foregoing method of finding the area of counties and kingdoms, 
must of course, be liable to considerable inaccuracy, not only as regards the 
method of taking the dimensions, but also as respects the correctness of the 
map and scale ; for it is evident that if these be not truly delineated, the 
dimensions can never be obtained to any degree of accuracy. 

3. — When you have a correct map and scale of a county or a kingdom, its 
content may be found to a considerable degree of accuracy by the following 
method : Divide the map into triangles and trapeziums in the most convenient 
manner ; and straighten the crooked shores or coasts, either with a lantern 
horn, as directed in Part IV., or by the parallel ruler, as directed in Part V. 
Measure the bases, diagonals, and perpendiculars correctly, by the scale of 
miles belonging to the map ; find the area of each figure separately • and 
the sum of these areas will be the whole area required* 



Section III.) land-surveying. 367 



EXAMPLES. 



1 . Suppose the mean length of a common or moor be esti- 
mated at 3} miles, and its mean breadth at 2± miles ; what is 
the area in acres, according to this estimation ? 



miles. 

3.75 

2.25 



1875 
750 
750 

8.4375 miles. 
640 

3375000 
506250 



5400.0000 acres. 



Ans. 5400 acres. 



2. If the mean length of a lordship be estimated at 4| miles, 
and its mean breadth at 2 J miles; what is the content in miles 
and acres? Ans. 10.625 miles, and 6800 acres. 

3. The mean length of a county, found from a map, is 63 
miles, and its mean breadth 42 miles ; what is its area in miles 
and acres ? Ans. 2646 miles, and 1693440 acres. 

4. Mr. Pinkerton says, in his Geography, that the content 
of Ireland is computed at 27457 square miles ; Avhat is its area 
in acres? Ans. 17,572,480 acres. 

5. According to Mr. Pinkerton, the content of Scotland is 
computed at 27793 square miles ; required its area in acres. 

Ans. 17,787,520 acres. 

6. The same author observes, that the extent of England and 
"Wales is computed at 58335 square miles ; what is the area in 
acres ? Ans. 37,334,400 acres. 



368 land-surveying. (Part VI. 

Note. — The real quantity of land in England is very uncertain ; and dif- 
ferent writers have given very different statements. Dr. Greve, in the Philo- 
sophical Transactions, No. 330, states the number of acres in England at 
46,000,000 ; but Sir William Petty, in his Political Arithmetic, states them 
at no more than 39,000,000. Dr. Halley's statement is also 39,000,000 acres ; 
but Zimmerman's statement, in his Political Survey, is only 34,631,080. 
Dr. Grew's statement stands at 46,800,000 ; and in the Gentleman's Maga- 
zine, for July, 1804, is a statement made from Smith's County Maps, by 
which the area is estimated at 32,134,400 acres. 

Now, if we take this number from the area of England and Wales, found 
in the last example, we shall have 5,200,000 acres for the area of Wales, 



LAND-SURVEYING. 



The Method of Measuring and Planning Villages, 
Towns, and Cities ; Directions for Measuring and 
Planning Building Ground, and Dividing it into con- 
venient Lots for Sale ; and Miscellaneous Questions 
relating to Surveying, Laying-out, Parting-ojf, and 
Dividing Land. 



SECTION I. 

THE METHOD OF MEASURING AND PLANNING VILLAGES, 
TOWNS, AND CITIES. 

As villages, towns, or cities, present themselves in almost 
every extensive survey, and are generally measured and planned 
with the adjoining or surrounding lands, it is highly necessary 
that something should be said on the method of taking and 
laying down the dimensions of such places, and finishing the 
plans. 

Besides, the plans of towns and cities are so essentially neces- 
sary for the purposes of commercial and general reference, that 
Surveyors are not unfrequently employed in forming correct 
drawings of the same, in order to have them engraved and 
published in copperplates. 

Without this art, we could not obtain the ichnography of 
towns and cities ; neither could we have any just idea of the 
shape, extent, and direction of the streets ; the size and number 
of the public buildings ; the local conveniences enjoyed by the 
inhabitants, &c. &c. of those places which circumstances will 
not permit us to visit. 

Bb 



370 LAND-SURVEYING. (Part VII. 

Directions for taking the Dimensions of Villages, Toicns, 
and Cities. 

The dimensions of villages, towns, and cities, may generally 
be obtained by the chain only ; as the streets are usually wide 
enough to admit of angles or tie-lines being taken -with the 
chain, at the meetings or intersections of the streets, in the 
same manner as directed in Problems 4 and 5, Part IV. In 
these Problems the methods of measuring meres, woods, roads, 
rivers, and canals, are clearly illustrated and exemplified ; and 
if the learner make himself completely master of those depart- 
ments of Surveying, any difficulties which may present them- 
selves in measuring villages, towns, or cities, will be easily sur • 
mounted. 

It will sometimes happen that the tie-lines cannot be mea- 
sured at a greater distance from the angular points than 30 or 
40 links. In such cases, the tie-lines must be taken to a quar- 
ter of a link, and both them and the angular distances must be 
multiplied by 2, 3, 4, or any larger number, as circumstances 
may require ; and the products used in laying down the chain- 
lines. (See Prob. 2, Part IV.) 

The notes taken in measuring towns and cities must be en- 
tered precisely in the same manner as in surveying estates ; and 
in measuring along the streets, offsets must be taken to the 
houses on both sides of the chain-line ; and particularly to 
every corner and projection ; even the small projections of 
bow-windows must not be omitted. 

Sketches of the bases of the buildings, particularly the corners 
and projections, must be made in the margin of the note-book, 
in order to assist the Surveyor in drawing a correct plan. 

All public buildings, such as churches, prisons, castles, court- 
houses, market-places, halls, colleges, mansion-houses, &c. &c. 
must be distinctly noticed ; and the range of the first line 
should be taken with the compass, in order that the Draftsman 
may be able to lay down every street in its true direction. 

Note 1 . — In measuring alonj: the streets, all the offsets to the buildings 
must be taken at right-angles to the chain-lines. The bases of the buildings, 
and all the projections must be sketched, as you proceed ; and the breadths 
r»f the buildings, the lengths and breadths of the projection?, fee. fee. must 



Sectio?l I.) LAND-SURVEYING. 371 

be correctly measured, and entered opposite to those parts of the sketch to 
which they respectively belong. The sign 4- (plus) is usually placed between 
the breadth of a building, at its perpendicular distance from the chain-line- 
The method of sketching the bases of buildings, and entering the notes, is 
exemplified in pages 4, 10, and 12, of the engraven Field-book, to which the 
learner is referred. 

2. — When a town and the surrounding or adjoining lands are both to be 
measured and planned together, the dimensions must be taken with Gunter's 
chain ; and the lines measured along the streets must be properly connected 
with those measured in surveying the adjoining estates ; but if the plan of a 
town only is required, it is more convenient to take the dimensions with a 
chain of 50 feet in length, divided into 50 links, and an offset staff of 10 feet 
in length. 

3. — As station staves cannot be fixed in the streets, in consequence of the 
pavement, they must either be set in wooden pedestals, made for that pur- 
pose, or two or more assistants must each hold a staff in those places that are 
pointed out by the Surveyor. 

4. — Sometimes it is most convenient to measure external or main-lines, 
on the outside of the town, as in surveying a mere or wood, Prob. 4, Part IV. ; 
and in running such lines, stations must be left at the ends of the streets, as 
you pass them, in order that lines may be run from one station to another 
in measuring the streets. 

5. — In some situations, and under certain circumstances, it is more eligible 
to measure the first line along one of the principal streets ; and to intersect 
this line by another, measured along some other principal street, nearly at 
right-angles with the former ; then these two lines being tied together by a 
connecting line, measured in the most convenient manner, will divide the 
town into four parts, each of which may be measured separately, by running 
lines in the most advantageous manner. (See a similar remark in Note 5, 
Method I. Part V.) 

6. — In putting down stations at the ends of the streets, &c. the number 
of the station may be made upon the wall of the opposite building, (if there 
be one,) with red or white chalk, in such a situation that an offset may be 
taken, at right-angles to the building, from the station marked upon the wall, 
to the station on the chain-line. This offset being entered in the book, and 
again measured from the station on the wall, at right-angles to the building, 
will give you the station on. the chain-line, whenever you may want to 
find it. 

7. — When the foregoing method cannot be adopted in consequence of not 
being able to take a right angled offset from any building to the station 
which you wish to fix, then two lines may be measured from the statiou to 

Bb 2 




b~2 i.A\'D-suRvtv.\\- (Part VII. 

or to any other parts of two adjoining buildings ; and the in- 
of these lines, when measured from the buildings, will give the 

r -: _ --. : 

- — _-_--.}r :.'.'. -'z- 77.7 - - ■ ' ---::- = '::.-- '~: ^7 7- -: ; :7 ; : . :'r.r- 77: :f:i :: 
the smaller and intermediate streets ; and lastly to the lanes, alleys, courts, 
yards, and every other part which it may be thought necessary to r c 
sent upon the plan. 

9. — When any of the streets are so narrow as not to admit of tie-lines 

"7.7.7. :ik-7~7:7 "7_r ••" ~.z- . t_t:-t; ~z:.z :z: :'. z~-Z-~zzz--. 77777 ~ .:::;:: 

■:t.t7. 7: -Zz 77.7 :7.:r- 7 :::::-::: .75 : 77 77777: - 77:.: '^ -.zziz zz If- 
grees and minutes, by a theodolite ; and in planning, they most be hud 
down as directed in Problems 20 and 21, Part I. (See the Description of die 
T~-e: i'l.r. 7777 : 74 

10. — "VThas has been advanced on tins subject will, no doubt, be aecepi- 

- .7 :: 't77t_77- "__: : = : :~ :_- 7: - ' zz: : ::77 -7:7. z z^z_- ::' 7 ".; 7-. 77:1 
: 7— 7777- ■ - 77 - : —_:J7 177 :Ji7ir :': 7777=. n: I7 ::. : n= zzzz '7 z\~-z\ :'zz: 
-■_". 7 7 7 7: 1- : . *:_7 :: 7-777 7-~ -— - ::-•: '-'- '~ t zz~: ~z:~z 77 77^:77:7. A 
7: :-:: ii-zl ~zLL z~z\ 7 777777 ~: :~ -7.7 777.: 777 7:77777: :: :'z- ~ 77-77 :r. 
who should, after duly examining every part of the town, endeavour to run 

7.r \\Z\-- 77 :77 77!-: 7 Z':ZZ': Z~ 7: 7_77 77 7 7 

Let it be required to measure the >~ 1 nra, No. 7, 

r -: VII. 

_:. -z-: :: :''. ~ -.:_--- : l-> ._-_' -; ". in X::-r -r. " r 5J12II 
begin at the south-west corner, as in Problem 4, Fir: TV.; 

-■.'.-.'l: '-Li- :i: - : :- I - zi ::;->". 7 in :"-f sin:- 

manner. if we begun at any other corner. 

F 1 z ■:.-. "."Ti — 1. : -Ir •" 

•iris :'z~ z I rz\-z : : :..._ f- ;-> :■: :i_f ' .:. tere- 

r it is necessary ; and sketching their bases in the margin 
of the note-book. At the end of High Street, 1 ui down — _ 
:-.: '^:..7 S: : i: L ; n-:. — ^ . -.- :L-r >. E. 

corner, -f- 5 ; and produce the Kne at pleasure, to — 

Second Lime. From -f 5, proceed towards the N . W. corner; 
but when you arrive at the end of Y rk Street, put down -f- 
and thence run a tie-line to -f- 6. From -f- ?, proceed with 
the main-line : and ax Km, Street, put down -{- 8 ; at George 
Street, + 9 ; at the N. W. comer, — 10; and continue the 
Hue to -f 11. 



Section I.) land-surveying. 373 

Third Line. From + 10, go towards the N. "W. corner; 
but when you come to the end of Low Street, put down + 12, 
from which run a tie -line to +11. Proceed from + 12 ; and 
at the end of Queen Street, put down + 13 ; at High Street, 
+ 14 ; and at the N. W. corner, + 15. 

Fourth Line. From + 15, proceed towards the S. W. cor- 
ner ; and at the end of George Street, put down + 16; at 
King Street, + 17 ; at York Street, + 18 ; and continuing 
the line to + 1, you will have circumscribed the town with 
four main-lines, into which the lines measured along the streets 
must be run. 

Note. — After the first three lines are laid down, it is evident that the fourth 
line will serve as a check ; and will reach exactly from + 15 to + 1, if all the 
operations have been conducted with accuracy. 

Fifth Line. From + 18, through York Street, to + 7. 

Sixth Line. From + 8, along King Street, to + 17. 

Seventh Line. From + 16, through George Street, to + 9. 

Eighth Line. From + 12, along Loav Street, to + 4. 

Ninth Line. From + 3, through Queen Street, to + 13. 

Tenth Line. From + 14, along High Street, to + 2 ; thus 
the survey of the town is completed. 

Note 1. — The chain-lines and stations do not appear upon the plan, as 
they could not have been conveniently entered without increasing its size ; 
the learner will, however, find no difficulty in making a similar plan, two or 
three times as large ; drawing the chain-lines, and putting down the stations 
in their proper places. Or he may take the dimensions of the given plan 
with a small scale ; enter them in a note-book ; and then draw a rough plan 
by a larger scale, and after that a finished one, which will be an exercise 
that will tend much to his improvement. 

2. — The survey of this town might have been carried on according to the 
directions given in Note 5, by measuring a line through King Street, and 
another through Queen Street ; and then connecting these two lines together 
by tie-lines taken at the point of intersection. Thus would the town be di- 
vided into four parts, each of which might be measured separately. 

3. — Here it will be proper to observe, that in taking an angle with the 
chain or theodolite, at the intersection or meeting of two lines, either the 
external or internal angle may be taken, as circumstances may make it most 
convenient ; but it should always be remembered, that neither very acute 
nor very obtuse angles should be measured, if it can be avoided, as both 
are liable to errors, in laying down. Those angles which approach nearest 
to right-angles should always be preferred, as being most correct. 

B b 3 



:J74- LAND-SURVEYING. (Pari VII. 

4. — By way of proof, it is an excellent plan to take both the angles. If 
they be taken by the chain, you will have a check-line, by the scale ; and if 
taken by the theodolite, their sum should be 180 degrees ; and you will 
also have a proof in planning, in consequence of having measured an angle 
and its supplement. (See Definition 16, and Problems 20 and 21, Part I.) 



A Descry . ./" Theodolite. 

The theodolite is a mathematical instrument used by Sur- 
veyors, for taking horizontal-angles, in measuring meres, woods, 
roads, rivers, canals, villages, towns, cities, &c. Sec. when tie- 
lines cannot be taken by the chain, in consequence of ob- 
structions. It also enables us to take such angles as are neces- 
sary for calculating the heights and distances of remote objects 
by plane trigonometry. 

There are various forms of this instrument, arising from the 
successive improi sments of many eminent artists ; but the prin- 
eiple of its operation is the same in all, whatever difference may 
appear in the construction. 

A theodolite of the best kind consists of the following prin- 
cipal parts : 

1 . A telescope to direct the sight, and enable the operator to 
distinguish objects at a distance. To the telescope is attached 
a sperit-level, to assist the operator in placing the instrument 
in a horizontal position. 

2. A vertical arc for taking angles of altitude and depression. 
One side of this arc is graduated to every half degree ; and 

these are again subdivided to every minute of a degree by the 
index or nonius. This side is numbered from to 90 decrees 
towards the eye-end, for angles of altitude ; and from to 50 
degrees, towards the object-end, for angles of depression. 

The other side of the vertical arc contains a line of divisions, 
showing the number of links to be deducted from each chain's 
length, in measuring up or down any ascent or descent, in order 
to reduce it to a true horizontal line, according to the directions 
given for surveying hilly ground, Method I, Part IV. 

3. A horizontal limb and compass, for taking horizontal- 
angles, and the bearings of objects. 



Section I.J land-surveying. 375 

The horizontal limb consists of two circular plates, one mova- 
ble on the other ; and the outer edge of the upper plate con- 
tains an index to the degrees and minutes on the lower plate. 
The upper plate, together with the compass, vertical arc, tele- 
scope, and level, are easily turned round upon a centre. 

The lower plate of the horizontal limb, is divided to half de- 
grees ; and these are again subdivided, by the scale of the no- 
nius, to every minute of a degree. 

This limb is numbered from the right-hand towards the left, 
with 10, 20, 80, 40, &c. to 3S0 degrees. 

4. The whole instrument fits on the conical ferril of a strong, 
brass-headed staff, with three substantial wooden legs, by which 
it can be firmly fixed upon the ground. 

The top or head of the staff, consists of two brass plates, pa- 
rallel to each other ; and four screws pass through the upper 
plate, and rest upon the lower plate. By the action of these 
screws, the situation of the upper plate may be varied, so as 
to set the horizontal limb truly level, or in a plane parallel to 
the horizon. 

Note 1. — The compass is fixed on the tipper plate of the horizontal limb ; 
and the ring of the compass is divided into 360 degrees, which are numbered 
in a direction contrary to those on the hox'izontal limb. The bottom of the 
compass-box is divided into four parts or quadrants, each of which is subdi- 
vided to every 10 degrees ; and numbered from the meridian, or north and 
south points, each way, to the east and west points. In the middle of the 
box is a steel pin, finely pointed, on which is placed the magnetic needle. 
The box also contains a small sperit-level, fixed at right-angles to that which 
is attached to the telescope. By the assistance of these two levels, and the 
four screws before mentioned, the instrument can be placed in a truly hori- 
zontal position. (See the Description of the Compass, Part II.) 

2. — The method of using the theodolite may soon be acquired by a little 
practice in the field ; but it will be obtained still more easily if the learner 
be assisted by the instructions of a practical operator. 

3. — When trigonometrical calculations are to be made from the angles, 
they should, if possible, be taken to a minute ; but an instrument that will 
take an angle to five minutes will answer very well for a practical Surveyor ; 
as angles cannot be laid down nearer, either by the line of chords or the 
protractor. 

4. — In order to lay down an angle by the protractor, draw a line at plea- 
sure, for one side of the angle ; apply the diameter of the instrument to this 

B b 4 



376 land-surveying. (Part VII. 

line, and its centre to the point where the angle is co be made ; mark the 
point under the given degree, and through this point draw the other side 
of the angle. 

5. — To measure a given angle by the protractor, apply the diameter to 
one side, and the centre to the angular point ; and the degree of the 
limb under which the other side passes, is the measure of the angle. (See 
Problems 19, 20, 21, 22, and 23, Part I.) 

6. — The following prices stand in Mr. Jones's Catalogue, for theodolites 
of different kinds ; viz. a common theodolite, without rack-work, the hori- 
zontal limb six inches in diameter, eight guineas. Ditto, with rack-work 
movements, and which will take angles to two minutes of a degree, twelve 
guineas. Second best 7 or 8-inch theodolites, which will take angles to a 
minute, sixteen guineas, and =£22 : Is. Very best improved ditto, £33 : 12s, 
Eight-inch ditto, £37 : 16s. Nine-inch ditto, £42. 



Directions for Planning Villages, Toicns, and Cities. 
All the main-lines must first be laid down ; and the stations 
upon them marked off. The lines measured along the streets 
must then he drawn ; and the stations upon them denoted, 
The bases of the buildings must next be laid down from the 
offsets, so as to form the streets; and shaded as directed in 
Part Y., and exhibited in Plate VII, The rough plan must 
then be transferred to a clean sheet, by some of the methods 
described in Part Y., in order to make a finished plan. 

The bases of all public buildings, such as churches, castles, 
prisons, session-houses, market-places, infirmaries, hospitals, 
mansion-houses, monuments, &c. &c. should be delineated upon 
the plan with the utmost correctness ; and most Surveyors draw 
the bases of the columns which support the roofs of market- 
crosses, the galleries of churches, &c. &c. as exhibited in the 
plate to which we last referred. 

The streets are usually left white ; but some draftsmen pre- 
fer colouring the causeways, with a tint of blue, to distinguish 
them from the carriage-roads, which are generally washed with 
a yellowish brown. 

The grass-plots, in gardens, public squares, &c. &c. whether 
they be rectangles, rhombuses, circles, ovals, or regular poly- 
gons, should be correctly delineated upon the plan; then 
shaded with Indian ink, and washed with green- *- *he same 



Section I.) land-surveying. 377 

manner as pasture-grounds ; and trees, water, pleasure-grounds 
gardens, gravel-walks, &c. &c. must be shaded and coloured 
as directed in Part V. 

The name of the village, town, or city, should he given in 
conspicuous characters, in some vacant part of the plan or map ; 
and the names of all the streets, public squares, churches, 
colleges, halls, prisons, castles, court-houses, mansion-houses, 
market-places, lanes, alleys, courts, yards, &c. &c. must be en- 
tered in their respective situations, in the manner exhibited in 
Plate VII. 

Note 1. — If the dimensions be taken and laid down in feet, a scale of feet 
must be given ; if in yards, a scale of yards must be given ; if in chains and 
links, a scale of chains and links must be given ; and if the town or city be 
very large, a scale of miles and furlongs may be given upon the plan, for the 
purpose of measuring distances ; and as 220 yards make a furlong, the dis- 
tance of one place from another maybe easily obtained in miles and yards. 

2. — Any remarks or explanations that it may be thought necessary to give, 
may be entered in some vacant corner of the plan. 

3. — All plans, ornaments, &c. should first be drawn in pencil ; and it will 
tend much to the improvement of the learner, if he form all his printing, 
German text, and large-hand letters by the pencil also, and then finish 
them with Indian ink. 

4. — In forming letters, ornaments, &c. with the pencil, the lines and 
strokes should be made as fine as possible ; as the ink frequently runs upon 
the lead, when the pencil has been used too freely ; hence the necessity of 
applying Indian rubber after the outlines have been finely drawn with Indian 
ink, in order to remove the lead which is not covered by the ink, before we 
proceed to finish the letters, ornaments, &c. 

5. — If the pupil does not succeed well in his first attempt with the pencil, 
the letters, ornaments, &c. must be effaced with Indian rubber ; and he must 
repeat the process until he can form all the letters, devices, &c. correctly. 
(See Note 6, Page 250.) 

6. — Brookman and Langdon's prepared lead pencils, marked F, for fine 
drawing, will be found to answer well in making letters, ornaments, &c. ; as 
they are of a middling degree of hardness ; consequently the marks made 
by them may be easily effaced. (See Note 4, page 209.) 

7. — After practice has made the learner a proficient in penmanship, he 
will be able to print, text, and write more expeditiously, without the use of 
the pencil. 

8. — Here it may not be improper to caution the learner against a very 
common fault of young draftsmen j namely, that of making their lines and 



378 LAND-SURVEYING. (Part VII. 

letters too strong, both with pencil and ink. The lines, dots, and letters be- 
longing to wooden cuts should never be imitated by the learner, as they ara 
mostly too strong and rough ; but he should take for his pattern the specimens 
exhibited in the different copperplates, given in this Work. 

9. — In Part the Second, ivory plotting-scales are recommended, as being 
the best ; but it may be proper to observe that very good feather-edged plot- 
ting scales are now made of box, by most mathematical instrument-makers, 
which will do very well for school-boys. A twelve inch box scale may be 
had for about four shillings ; but an ivory scale of the same length costs 
ten or twelve shillings, accordingly as it is finished. 

10. — What has been said on the subject of planning villages, towns, and 
cities, will be further illustrated by examining the plan of some large village, 
town, or city. The author recommends to those who desire to increase their 
information on this subject, a small plan of Leeds, neatly engraved ; and sold 
by J. Heaton, Leeds, price 2s. ; a large, elegant, coloured plan of Leeds, con- 
taining all the recent improvements ; published by Longman and Co. London, 
price 21s. ; a small plan of London, neatly engraved, price 2s. 6d. ; also a 
new coloured plan of London, with its environs, including the surrounding 
villages. In this plan all the new roads, streets, buildings, bridges, squares, 
&c. &c. have been accurately inserted from original and actual surveys ; 
together with the projected improvements not yet-executed. Both these 
plans are published by Laurie and Whittle, London ; the latter on a large 
sheet, price 6s. In this plan, the bases of houses are shaded with dots, in 
imitation of sand, as in the lower part of No. 2 ; but the bases of public 
buildings are shaded with lines, as in No. 7, Plate VII. The plan is sur- 
rounded by a border, which is divided into miles ; and each mile is subdi- 
vided into eight equal parts or furlongs. 

Besides the above maps, it may be proper to observe that an excellent 
coloured plan of London and its vicinity, has lately been published by 
W. Darton, No. 58, Holborn Hill, London, on one large sheet, price 6s. 6d. 
A plan of Edinburgh might also be consulted with considerable advantage, 
by the young Surveyor ; as the new town is laid out with remarkable regu- 
larity and elegance. 

TO CLEAN PLANS OR MAPS. 

It has been intimated to the young draftsman, in Note 6, 
page 250, that every precaution should be taken to keep plans 
and maps clean, in executing them : but notwithstanding the 
greatest possible care be exercised, they will generally be some- 
what soiled, (perhaps in consequence of misfortunes,) either by 
dust, ink, or colours ; hence it is necessary to give the method 
of cleaning them after they are finished. 



Section I.J land-surveying. S79 

Note. — Not only the face but also the back of a plan should be cleaned, 
in order to make it look as well as possible ; and give it the appearance of 
coming from the hands of a neat and elegant draftsman. 



To clean Plans or Maps that are soiled with Dust, Indian Ink, 
or Colours. 

Take a sharp penknife, with a roundish point, and scrape 
those parts gently which are besmeared with ink or colours, 
until you efface the blots ; then use clean Indian rubber freely 
to those places that are soiled with dust ; and lastly, rub the 
whole map well with white bread ; taking care to pare the 
bread as it accumulates the dust. 

Note 1. — Indian rubber is made from the juice of a large and much 
branched tree, which grows in Guiana, Cayenne, and other parts of South 
America. The juice is obtained by making incisions through the bark of the 
tree, chiefly in wet weather. From the wounds thus formed, the juice, which 
is of a whitish colour, flows abundantly. It is usually brought to Europe in 
the form of pear-shaped bottles, which are made by spreading the juice over 
moulds of clay. These exposed to a dense smoke^ or to a fire, till they 
become so dry as not to stick to the fingers ; and then by certain instruments 
of iron or wood, they are ornamented on the outside with various figures. 
This done, the clay, in the inside, is moistened with water, and then picked 
out by proper instruments. 

2. — When Indian rubber has become foul by frequent use, it may be 
cleaned by washing it in lukewarm water and soap. 

To clean Plans or Maps that are blotted with Common Ink. 

If the blots be light, they may be scraped out with a pen- 
knife, or effaced by rubbing them repeatedly with clean paper 
wet in water or saliva ; but when they are deep, acid or salt of 
lemons must be used in the following manner : Dissolve a small 
portion of the acid in hot water, and with a clean hair-pencil, 
dipped in the solution, wash the blots until they are discharged. 

Note 1. — Recent blots are easily obliterated ; but when they are old, and 
very deep, it will be found necessary to let the paper dry, and repeat the 
wash several times. Salt of lemons is sold in small boxes, by druggists. 

2. — When you have to write upon those places from which the blots have 
been removed, the paper will bear the ink better, if you rub a little pounce 
upon it, with clean paper ; and then smooth it with your folder, or with the 




-_Lr - Li- 







r:: 1 



SECTION II. 



MSECTIOXS FOR MZEASTRi: ANL PLAXXIl 3U1LDLSG 
GSOUXD, AXT> DITLDIXG IT ISTO COXTESTEyT LOTS 
FOB SALE. 



L -:r ■ ; J."..:: - . - ■ ':' .: - 



L-lxd lying in dbe TkEnrj of large tonus, is frequently sold 

' - -'i- : .n:t 71J:. : : ' _ Liz^-r: : — - :-- - 1= -- --~^ ": -~~ 
a h%ft pice when ike saiadon is e%£Ue. k is of ike greatest 
tan to die toner and aeflo. to ascertain is 



Section II.) land-surveying. 381 

In order to accomplish this desirable object, the dimensions 
should be very correctly taken, with a measuring-tape, divided 
into yards, tenths, and hundredths ; or with a tape divided into 
feet and tenths, or feet and inches. 

When the dimensions are taken in feet and inches, the inches 
must be reduced to the decimal parts of a foot ; and the area 
found from such dimensions, must be divided by 9, to bring it 
into square yards. 

Whatever be the shape of the ground to be measured, it must 
be divided into such squares, rectangles, trapezoids, trapeziums, 
or triangles, as will give the true content of the whole ; and if 
the sides be crooked, offsets must be taken as directed in Pro- 
blem 6, Part III. 

Narrow pieces of building-ground must be measured by Pro- 
blem 7 ; and if they be very irregular, their areas may be cor- 
rectly found by the method of equidistant ordinates described 
in Problem 9, Part III. 

Note 1. — As a measuring-tape is not so convenient in taking the dimen- 
sions of land as a chain, it is more eligible to use the latter when the land to 
he measured is extensive ; the greatest care, however, must be used in order to 
obtain the dimensions correctly, which should be taken to a quarter of a link, 

2. — The chain must be completely stretched, and held at the bottom of the 
arrows, in measuring ; and if it be an inch or two over long, an allowance 
must be made in the dimensions : thus, if a line of 650 links be measured by 
a chain that is 2} 2 inches above 66 feet, we shall have 6^x2^ = 161 inches 
i= 2 links nearly ; hence the true length of the line will be 652 links. 

3. — The above method may also be adopted in measuring land, when it is 
found necessary to correct the dimensions taken by a chain that exceeds the 
proper length. (See the Description of the Chain, Part II.) 

4.— As 4840 square yards make 1 acre, 1210 square yards 1 rood, and 
30 i square yards 1 perch, we can easily reduce acres, roods, and perches 
to square yards, in the following manner : Multiply 4840 by the number of 
acres ; 1210 by the number of roods ; and 30.25 by the number of perches ; 
then the sum of these three products will be the square yards required. 

5. — When the area is in square links, divide it by 20.6611, the number of 
square links in a square yard ; and the quotient will be the area in square 
yards. (See the Table of Square Measures in Tart III.) 



382 land-surveying. (Part VII 

fi. — Building-ground is generally sold in small parcels. Sometimes, how- 
ever, it is sold by whole fields together, which are afterwards divided by the 
buyer, and retailed out in small lots. 



EXAMPLES. 

1. The length of a rectangular piece of building -ground is 
65.8 yards, and its breadth 32.6 yards ; "what is its area in 
square yards, and its value at .5s. 9d. per square yard ? 

Yds. 
65. S 
•32.6 

3948 
1316 
1974 



2145.08 Area. 



yd. s. vds. £. s. d. 

As"l : 5.75 :: 2145.08 : 616 14 2 J the value. 



2. The length of a rectangle measures £5.36, and its breadth 
43.28 yards ; what is its area in square yards, and its value at 
6s. 3d. per square yard ? 

Ans. The area is 3694.3808 square yards ; and the value of 
the land £1154. 9s. 10id. 

3. The parallel sides of a piece of ground in the form of a 
trapezoid, measure 84.63, and 72.78 yards, and the perpendi- 
cular distance between them 56.59 yards ; what is its area in 
square yards ? Ans. 4453.91595 square yards. 

4. The diagonal of a trapezium measures 236.5 feet, one of 
the perpendiculars 189.3 feet, and the other 127.9 feet; what 
is its area in square yards ; and its value at £l. 6s. 6d. per 
square yard ? 

Ans. The area is 4167.655 square yards; and the value of 
the ground £5522. 2s. lOjd. 

5. The base of a triangle measures 369.9 feet, and the per- 
pendicular 234.7 feet ; what is its area in square yards, and its 
value at 2s. 6d. per square yard ? 

Ans. The area is 4823.085 square yards; and the value 
«£602. 17s. 8|d. 



Section II.) land-suuveying. 383 

6. The three sides of a triangle measure 362 feet 3 inches, 
316 feet 6 inches, and 284 feet 9 inches respectively; what is 
its area in square } r ards ? 

Ans. By Note 4, Part IV., you will find the area to be 4810 
square yards. 

7. Draw a plan of an irregular piece of land, and find its 
area in square yards, from the following dimensions, taken in 
feet. 





AB 





1286 


247.6 


1015 




987 




790 


317.6 


720 




560 


223.5 


465 




346 


345.2 


268 


372.4 


000 


Begin 


at A, and 



145.6 

5Q.8 
136.5 

164.2 

124.8 

245.3 
go West, 



Answer. 

Dcuhle Areas. 

359147.3 Offsets on the right. 
676164.8 Ditto on the left. 



2)1035312.1 Sum. 
9)517656.05 Area in square feet. 
57517.33 Ditto in square yards. 



8. Required the plan of a piece of building-ground, and also 
its area in square yards, from the following equidistant ordi- 
nates, taken in feet. 



— 



L->UKTtYI ft VII 





A z 


:■:■:? 


~ i < 


_ 


:•« * 


:-.■ - 


; ■*•" 


?■':.'* 


■ 


:: : 


- ; '•" 


. : 


"•'-: 




- 


; • ' 


:. • 




: 




I • 


: ; : 


vr 


- -r"- 


i- A_ I" . 



1 ~ -~-' 




: : : : ; -- 



----- 



z z li r : _ — _' 




15- 7 






Section II) land-surveying, 



385 



Answer. 
Double Areas. 

658576.8 Triangle ABC. 
81307.2 Offsets on B C. 



2)739884.0 



9)369942.0 Area in square feet 
41104.6 Ditto in square yards. 

10. Required the plan of a portion of building-ground, and 
also its area in square yards, from the following dimensions, 
taken by Gunter's chain ; likewise its value, supposing it to 
have been sold by auction, at 14s. 9d, per square yard. 





BD 






1235 






1075 


4741 A 


C482I 


270 
R. off B. 






AB 




221 


1175 




25 \ 


1100 




45| 


1000 




m 


900 




54| 


800 




681 


700 




701 


600 




65| 


500 




60i 


400 




55\ 


300 




40f 


200 




321 


100 







000 




Begin 


at A, and 


go Wesi 



Note. — In calculating the area, the 'quarter-links must be treated 
decimals. 

Answer, 

Double Areas. 
1181895.00 Trapezium ABCD. 
112881.25 Offsets on A B. 

2)12917 76^25 Sum. 
647388.125 Area square links. 



c c 



386 LAND-SURVEYING. (Tori VII 

By note 5. we have 647388,125 -r 20.6611 = 31333.67. the 
area in square yards; then, as 1 yd. : 14.75s. :: 31333.67 yds. 
: 462171. 6325s. = 23M $£. lis. 7§<L the value required. 



BvUdlivi-oroun'L and Dividing it into 
. . L Is for Sbln 

Building-ground may be laid down by a plotting-scale, 
whether the dimensions be taken in yards or in feet, by calling 
each chain upon the scale, one yard, or one foot, as the case 
requires ; and the intermediate divisions will evidently be 
tenths of a yard, or tenths of a foot. 

If the plot of ground be small, the scale made choice of 
should be pretty large, so as to make the ground, on the plan, 
appear to the best advantage; and exhibit every part dis- 
tinctly. 

After the plan has been drawn, the ground must be judi- 
ciously divided and laid out, by making streets at a proper dis- 
tance frGrn each other ; and then subdivided into convenient 
parcels or lots for sale, according to the situation of the place, 
and the size of the houses for which the ground is best adapted. 

Main or principal streets should be much wider than it is 
necessary to make back or intermediate streets ; and the size 
of house-steads adjoining main streets should exceed the size 
of those adjoining back streets. 

TThen it is practicable, all streets should be laid out in straight 
lines ; and if possible, their intersections should be always at 
right-angles to each other ; because straight streets are not only 
more beautiful than crooked ones, but also more commodious 
for business. Many of our old towns make a wTetched ap- 
pearance in consequence of the crookedness, narrowness, and 
irregularity of the streets. 

Streets are laid out of very different breadths, from 1.5 to 90 
or 100 feet; but when ground is of great value, the breadth 
of the streets becomes an object of serious consideration, whether 
the ground, occupied by them, be given by the seller, or pur- 
chased by the buver of the adjoining: lots. 



Section II) land-surveying. 387 

Building-ground may sometimes be very elegantly laid out 
in a square or a rectangle. When this is the case, the houses 
are built on the margin or outside of the square ; and in the 
middle is left an open area, which is generally ornamented with 
grass-plots, gravel walks, trees, &c. 

If the ground will admit, it is very desirable for each house 
to have a garden laid out in the front ; which must, of course, 
be sold with the house-stead. The open area may be divided 
into as many equal parts, as there are house-steads in the 
square ; one part may be sold with each house -stead ; and the 
respective purchasers may occupy the whole as joint property. 

Ground laid out in this manner, generally fetches a good 
price, as most persons think it more pleasant and healthful 
living in squares than in streets. 

After every thing has been properly and judiciously arranged 
upon the plan, such dimensions must be taken by the scale as 
will enable the Surveyor to stake out all the streets, squares, 
lots, house-steads, &c. &c. in the field. This being done, the 
ground may then be considered as ready for inspection and sale. 

Note 1 . — House-steads must be laid out of different sizes, according to the 
respectability of the intended buildings. A room 14 by 15 feet will be found 
quite large enough for any cottage ; and these dimensions may be increased 
at pleasure, to 20 or 24 feet, according to situation and circumstances. 

2. — A plan of ground or buildings, intended for sale, is generally left for 
inspection, at the office of the surveyor or solicitor, employed on the occa- 
sion, from the time of advertising to the time of sale. Also, the special con- 
ditions of the sale, not specified in the advertisement, may commonly be 
known at those offices ; or by applying to the proprietor, or to his agent, 
previously to the day of sale. 

3. — Building-ground is generally sold by auction ; and if it be divided 
into small lots, it will tend much to promote the sale ; as many persons may 
be desirous of purchasing a single house-stead, who would not find it con- 
venient to purchase a lot containing two or three house-steads. 

4. — The price of building-ground varies from sixpence to upwards of two 
guineas per square yard, according to the eligibility of the situation. 

5. — The method of laying out building-ground so as to form straight 
streets at right-angles to each other, is exemplified in the Plan of a new 
Town, Plate VII. This town bears a considerable resemblance to Somers- 
town, and to Pentonville, near London. 

c c 2 



388 LAND-SUKVEYING. (Part VII. 



SECTION III. 

Miscellaneous Questions relating to Surveying, Laying-out. 
Parting-ojf, and Dividing Land. 

1. The base of the largest Egyptian pyramid is a square, 
whose side is 693 feet ; how many acres of ground does it 
cover? Ans. 11a. 0/-. 4p. 

2. Required the side of a square garden that cost 31. 18s. l\d. 
trenching, at l\d. per square yard. Ans: 25 yards. 

3. Required the area of a rectangle whose length is 127-5, 
and breadth 675 links. Ans. Sa. 2r. 17/>. 

4. The area of a rectangular field is l±a. 2r. lip. ; what is its 
length, its breadth being 925 links ? Ans. 1575 links. 

5. A rectangular allotment upon a common, cost 78/. 1.?. lO^d. 
digging and levelling, at 11. 10s. per acre ; what will be the 
expense of fencing it half round, at 5s. 6d. per rood ; its length 
being 122.5 links ? Ans. 171. 18s. 8d. 

6. Measuring along the base of a field in the form of a rhoni- 
boides, I found the perpendicular to rise at 678, and its length 
1264 links ; the remainder of the base measured 2435 links; 
what is the area of the field ? Ans. 39a. Ir. 15£p. 

7. A grass-plot, in a gentleman's pleasure-ground, cost 
Si. 14.?. Id. making, at 4<7. per square yard; what is the length 
of the base, the perpendicular being 40 feet, and the figure a 
rhombus? Ans. 50 feet. 

8. What is the area of a triangular field, the base of which 
measures 3568 links, the perpendicular 1589 links, and the 
distance between one end of the base and the place of the per- 
pendicular 1495 links 1 Ans. 28a. Ir. 15lp. 

9. After measuring along the base of a triangle -895 links. 
I found the place of the perpendicular, and the perpendicular 
itself =994 links ; the whole base measured 1958 links ; what 
is the area of the triangle \ Ans. 9m. 2v\ 37//. 



Section III. J miscellaneous questions. 389 

10. The area of a triangle is 6 acres, 2 roods, and 8 perches, 
and its perpendicular measures 826 links ; what will be the 
expense of making a ditch, the whole length of its base, at 
2s. 6d. per rood? Ans. 61. 4s. 7^/. 

11. What is the area of a triangle whose 3 sides measure 
15, 20, and 25 chains respectively? Ans. 15 Acres. 

12. Required the area of a grass-plot in the form of an equi- 
lateral triangle, whose sidels 36 feet. Ans. 561. 18446 /<?<?Z. 

13. What is the area of a triangular field whose 3 sides 
measure 2564, 2345, and 2139 links? Ans. 23a. 2r. 0|p. 

14. The 3 sides of a triangular fish-pond measure 293, 
239, and 185 yards; what did the ground which it occupies 
cost, at 185/. per acre ? Ans. 843/. 7s. Sd. 

15. How many square yards of paying are there in a tra- 
pezium whose diagonal is found to measure 126 feet 3 inches, 
and perpendiculars 58 feet 6 inches, and 65 feet 9 inches ? 

Ans. 871.47569 yards. 

16. In taking the dimensions of a trapezium, I found the first 
perpendicular to rise at 568^ and to measure 835 links ; the 
second at 1865, and to measure 915 links; the whole diagonal 
measured 2543 links ; what is the area of the trapezium ? 

Ans. 22a. \r. 0j?. 

17. Lay down a trapezium, and find its area from the fol- 
lowing dimensions ; namely, the side A B measures 345, B C 
156, C D 323, D A 192, and the diagonal A C 438 feet. 

Ans. 52330.33406/^, 

18. What is the area of a trapezoid whose parallel sides mea- 
sure 25 and 18 feet ; and the perpendicular distance between 
them, 38 feet ? Ans. 1197 feet. 

19. The parallel sides of a piece of ground measure 856 and 
684 links, and their perpendicular distance 985 links ; what is 
its area? Ans. 7a. 2r. 13^;. 

20. If the parallel sides of a garden be 65 feet 6 inches, and 
49 feet 3 inches, and their perpendicular distance 56 feet 9 
inches ; what did it cost, at £325. 10s. per acre ? 

Ans. 2U. 6s. 7{d. 



390 jUAND-SURTEYINCL (Part VII 

21. It is required to lav down a pentangular field, and find its 
annual value a: . pet acre, the first side measuring . 
the second 536, the thi te fourth 628, fifth 
587 links : and the diagonal from the first angle to the 
third 1194. and that from the third to the fifth 1223 links. 

\ 

22. The diameters of an elliptical piece of ground ai- 
and 22 : '.-:■: ; how many quicks will plant the fence forming 
the circumference, supposing them U set 5 bodies ismi 

.4 - \ 

23. Given the lengths of ? equidistant ordinates of an 
irregular piece of ground, as follows ; 15, 19, 20, i _ 

the length of the isf '. feet; required the 
plan and area. Ans. IT I 

24. What must be the length of a chord which will strike 
the circumference of a circular plantation that shall contain 
just Em acre and a half of ground \ *_ 

_ " The annual rent of a triangular field is 4 1 5 its 
measure i'. rod perpendicular 14 chains: what is it lei ::: 
per &■:: 

The transverse diameter of the ellipse in Grosvenor- 
square measures 840 links, and the conjugate 612, within the 
wall ; the wall is 14 inches thick ; what quantity of ground 
does it inclose, and how much does it occupy ■ 

7 incloses £o. Bp. andocc 

IT 1 : 

Two sides :i an obtuse-angled triangle are 5 and 10 
chains ; what must be the length of the third side, that the 
triangle may contain just two acres of gi i- . 

3.06225 )14Q hams. 

28. What is the area of an isosceles triangle inscribed in a 
circle whose diameter is 24 : the angle included by the equal 
sides of the triangle being 30 degR An.?. 134.3-538. 

. i: -: ABof a triangular field is 40, B C 30, and 
C A 25 chains; required the sides of a triangle parted off by 



Section III.) miscellaneous questions. 391 

a division-fence made parallel to A B, and proceeding from a 
pointdn C A, at the distance of 9 chains from the angle A. 

Ans. 16, 19.2, and 25.6 chains. 

30. A field in the form of a right-angled triangle is to be 
divided between 2 persons, by a fence made from the right- 
angle, meeting the hypothenuse perpendicularly, at the distance 
of 880 links from one end; required the area of each person's 
share, the length of the division-fence being 660 links. 

Ans. 2a, Sr. 244/?. and la. 2r. 21^?. 

31. It is required to part from a triangular field whose 3 
sides measure 1200, 1000, and 800 links respectively, 1 acre, 
2 roods, and 16 perches, by a line parallel to the longest side. 

Ans. The sides of the remaining triangle are 
927, 7721, and 618 links respectively. 

32. The base of a field, in the form of a trapezoid, is 30, and 
the 2 perpendiculars are 28 and 16 chains respectively; it is 
required to divide it equally between 2 persons, by a fence 
parallel to the perpendiculars. 

Ans. The division -fence is 22.8035 chains ■, and 
it divides the base into two parts, ichose lengths 
are 17.0087 and 12.9913 chains respectively. 
33. A gentleman a garden had, 

Fivescore feet long and four score broad ; 

A walk of equal width half round 

He made, that took up half the ground : 

Ye skilful in geometry, 

Tell us how wide the walk must be. 

Ans. 25.96876 feet. 

Note 1. — If the sum of the two diameters of an ellipse be multiplied by 
1.5708, the product will be the circumference, exact enough for most prac- 
tical purposes. (See Question 22.) 

2. All the foregoing Questions are taken from the Author's Treatise on 
Practical Mensuration ; consequently, their Solutions may be found in the 
Key to that Work. 



392 



LAND-SURVEYING. (Part VII. 



ADDENDA. 

The following figure represents the chain-lines, forming the 
2 trapeziums and the triangle, in Example 6, page 152. — 
When the learner constructs the figure, he must of course lay 
down the offsets, from the notes ; and dot all the chain-lines, 
as before directed. 
E 




FINIS. 




FIELD-BOOK 



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Hantrgutbe^tng. 



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